線形代数例

$[\begin{array}{c} - \frac{1}{\sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2

分母を組み合わせて簡約します。

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ステップ 2.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 2.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 2.6.4.1

共通因数を約分します。

ステップ 2.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 2.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 3

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4

分母を組み合わせて簡約します。

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ステップ 4.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 4.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 4.6.4.1

共通因数を約分します。

ステップ 4.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 4.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 5

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 6.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 6.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 6.6.4.1

共通因数を約分します。

ステップ 6.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{1}} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 6.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 7

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 8.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 8.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 8.6.4.1

共通因数を約分します。

ステップ 8.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{1}} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 8.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 9

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 10.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 10.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 10.6.4.1

共通因数を約分します。

ステップ 10.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3^{1}} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 10.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 11

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 12.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 12.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 12.6.4.1

共通因数を約分します。

ステップ 12.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 12.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 13

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 14.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 14.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 14.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 14.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 15

タップして手順をさらに表示してください…

ステップ 15.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $3 \times 3$ and the second matrix is $3 \times 3$ .

ステップ 15.2

1番目の行列の各行と2番目の行列の各列を掛けます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ \frac{\sqrt{2}}{2} \cdot 1 + 0 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 + 0 \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 + 0 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ 0 \cdot 1 + \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 15.3

すべての式を掛けて、行列の各要素を簡約します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 16

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 17.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 17.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 17.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 17.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 18

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 19.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 19.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 19.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{1}} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 19.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 20

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 21.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 21.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 21.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2^{1}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 21.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 22

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 23.1

$\frac{1}{\sqrt{2}}$ に $\frac{\sqrt{2}}{\sqrt{2}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.2

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.3

$\sqrt{2}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6

${\sqrt{2}}^{2}$ を $2$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 23.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{2}$ を $2^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 23.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 23.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 24

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 25.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 25.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 25.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 25.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 26

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 27.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 27.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6.4

$2$ の共通因数を約分します。

タップして手順をさらに表示してください…

ステップ 27.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 27.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \end{array}]$

ステップ 28

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}]$

ステップ 29

分母を組み合わせて簡約します。

タップして手順をさらに表示してください…

ステップ 29.1

$\frac{1}{\sqrt{3}}$ に $\frac{\sqrt{3}}{\sqrt{3}}$ をかけます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}]$

ステップ 29.2

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}]$

ステップ 29.3

$\sqrt{3}$ を $1$ 乗します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}]$

ステップ 29.4

べき乗則 $a^{m} a^{n} = a^{m + n}$ を利用して指数を組み合わせます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}]$

ステップ 29.5

$1$ と $1$ をたし算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}]$

ステップ 29.6

${\sqrt{3}}^{2}$ を $3$ に書き換えます。

タップして手順をさらに表示してください…

ステップ 29.6.1

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ を利用し、 $\sqrt{3}$ を $3^{\frac{1}{2}}$ に書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}]$

ステップ 29.6.2

べき乗則を当てはめて、指数 ${(a^{m})}^{n} = a^{m n}$ をかけ算します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}]$

ステップ 29.6.3

$\frac{1}{2}$ と $2$ をまとめます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

ステップ 29.6.4

$2$ の共通因数を約分します。

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ステップ 29.6.4.1

共通因数を約分します。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

ステップ 29.6.4.2

式を書き換えます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} \end{array}]$

ステップ 29.6.5

指数を求めます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$

ステップ 30

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & 0 & \frac{4 \sqrt{3}}{3} \\ 0 & \frac{\sqrt{2}}{2} & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$ を掛けます。

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ステップ 30.1

ステップ 30.2

1番目の行列の各行と2番目の行列の各列を掛けます。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2} \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + 0 (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + 0 \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot 0 + 0 \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ 0 (- \frac{\sqrt{2}}{2}) + \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} \cdot 0 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \cdot 0 + \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \end{array}]$

ステップ 30.3

すべての式を掛けて、行列の各要素を簡約します。

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ステップ 30.3.1

$4$ に $2$ をかけます。

$[\begin{array}{c} \frac{7}{3} & \frac{5}{6} & \frac{5}{6} \\ \frac{5}{6} & \frac{11}{6} & \frac{4}{3} \\ \frac{5}{6} & \frac{4}{3} & \frac{3 + 8}{6} \end{array}]$

ステップ 30.3.2

$3$ と $8$ をたし算します。

$[\begin{array}{c} \frac{7}{3} & \frac{5}{6} & \frac{5}{6} \\ \frac{5}{6} & \frac{11}{6} & \frac{4}{3} \\ \frac{5}{6} & \frac{4}{3} & \frac{11}{6} \end{array}]$

線形代数 例

線形代数例