有限数学示例

$[\begin{array}{c} 10 & 20 & 25 & 1 & 0 & 54300 \\ 12 & 6 & 15 & 0 & 1 & 33480 \\ - 8 & - 16 & - 40 & 0 & 0 & 0 \end{array}]$

解题步骤 1

Multiply each element of $R_{1}$ by $\frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

点击获取更多步骤...

解题步骤 1.1

Multiply each element of $R_{1}$ by $\frac{1}{10}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{10}{10} & \frac{20}{10} & \frac{25}{10} & \frac{1}{10} & \frac{0}{10} & \frac{54300}{10} \\ 12 & 6 & 15 & 0 & 1 & 33480 \\ - 8 & - 16 & - 40 & 0 & 0 & 0 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 12 & 6 & 15 & 0 & 1 & 33480 \\ - 8 & - 16 & - 40 & 0 & 0 & 0 \end{array}]$

解题步骤 2

Perform the row operation $R_{2} = R_{2} - 12 R_{1}$ to make the entry at $2, 1$ a $0$ .

点击获取更多步骤...

解题步骤 2.1

Perform the row operation $R_{2} = R_{2} - 12 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 12 - 12 \cdot 1 & 6 - 12 \cdot 2 & 15 - 12 (\frac{5}{2}) & 0 - 12 (\frac{1}{10}) & 1 - 12 \cdot 0 & 33480 - 12 \cdot 5430 \\ - 8 & - 16 & - 40 & 0 & 0 & 0 \end{array}]$

解题步骤 2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & - 18 & - 15 & - \frac{6}{5} & 1 & - 31680 \\ - 8 & - 16 & - 40 & 0 & 0 & 0 \end{array}]$

解题步骤 3

Perform the row operation $R_{3} = R_{3} + 8 R_{1}$ to make the entry at $3, 1$ a $0$ .

点击获取更多步骤...

解题步骤 3.1

Perform the row operation $R_{3} = R_{3} + 8 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & - 18 & - 15 & - \frac{6}{5} & 1 & - 31680 \\ - 8 + 8 \cdot 1 & - 16 + 8 \cdot 2 & - 40 + 8 (\frac{5}{2}) & 0 + 8 (\frac{1}{10}) & 0 + 8 \cdot 0 & 0 + 8 \cdot 5430 \end{array}]$

解题步骤 3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & - 18 & - 15 & - \frac{6}{5} & 1 & - 31680 \\ 0 & 0 & - 20 & \frac{4}{5} & 0 & 43440 \end{array}]$

解题步骤 4

Multiply each element of $R_{2}$ by $- \frac{1}{18}$ to make the entry at $2, 2$ a $1$ .

点击获取更多步骤...

解题步骤 4.1

Multiply each element of $R_{2}$ by $- \frac{1}{18}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ - \frac{1}{18} \cdot 0 & - \frac{1}{18} \cdot - 18 & - \frac{1}{18} \cdot - 15 & - \frac{1}{18} (- \frac{6}{5}) & - \frac{1}{18} \cdot 1 & - \frac{1}{18} \cdot - 31680 \\ 0 & 0 & - 20 & \frac{4}{5} & 0 & 43440 \end{array}]$

解题步骤 4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & 1 & \frac{5}{6} & \frac{1}{15} & - \frac{1}{18} & 1760 \\ 0 & 0 & - 20 & \frac{4}{5} & 0 & 43440 \end{array}]$

解题步骤 5

Multiply each element of $R_{3}$ by $- \frac{1}{20}$ to make the entry at $3, 3$ a $1$ .

点击获取更多步骤...

解题步骤 5.1

Multiply each element of $R_{3}$ by $- \frac{1}{20}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & 1 & \frac{5}{6} & \frac{1}{15} & - \frac{1}{18} & 1760 \\ - \frac{1}{20} \cdot 0 & - \frac{1}{20} \cdot 0 & - \frac{1}{20} \cdot - 20 & - \frac{1}{20} \cdot \frac{4}{5} & - \frac{1}{20} \cdot 0 & - \frac{1}{20} \cdot 43440 \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & 1 & \frac{5}{6} & \frac{1}{15} & - \frac{1}{18} & 1760 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 6

Perform the row operation $R_{2} = R_{2} - \frac{5}{6} R_{3}$ to make the entry at $2, 3$ a $0$ .

点击获取更多步骤...

解题步骤 6.1

Perform the row operation $R_{2} = R_{2} - \frac{5}{6} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 - \frac{5}{6} \cdot 0 & 1 - \frac{5}{6} \cdot 0 & \frac{5}{6} - \frac{5}{6} \cdot 1 & \frac{1}{15} - \frac{5}{6} (- \frac{1}{25}) & - \frac{1}{18} - \frac{5}{6} \cdot 0 & 1760 - \frac{5}{6} \cdot - 2172 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 6.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & \frac{5}{2} & \frac{1}{10} & 0 & 5430 \\ 0 & 1 & 0 & \frac{1}{10} & - \frac{1}{18} & 3570 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 7

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{3}$ to make the entry at $1, 3$ a $0$ .

点击获取更多步骤...

解题步骤 7.1

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - \frac{5}{2} \cdot 0 & 2 - \frac{5}{2} \cdot 0 & \frac{5}{2} - \frac{5}{2} \cdot 1 & \frac{1}{10} - \frac{5}{2} (- \frac{1}{25}) & 0 - \frac{5}{2} \cdot 0 & 5430 - \frac{5}{2} \cdot - 2172 \\ 0 & 1 & 0 & \frac{1}{10} & - \frac{1}{18} & 3570 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 7.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 2 & 0 & \frac{1}{5} & 0 & 10860 \\ 0 & 1 & 0 & \frac{1}{10} & - \frac{1}{18} & 3570 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 8

Perform the row operation $R_{1} = R_{1} - 2 R_{2}$ to make the entry at $1, 2$ a $0$ .

点击获取更多步骤...

解题步骤 8.1

Perform the row operation $R_{1} = R_{1} - 2 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 0 - 2 \cdot 0 & \frac{1}{5} - 2 (\frac{1}{10}) & 0 - 2 (- \frac{1}{18}) & 10860 - 2 \cdot 3570 \\ 0 & 1 & 0 & \frac{1}{10} & - \frac{1}{18} & 3570 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

解题步骤 8.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0 & 0 & 0 & \frac{1}{9} & 3720 \\ 0 & 1 & 0 & \frac{1}{10} & - \frac{1}{18} & 3570 \\ 0 & 0 & 1 & - \frac{1}{25} & 0 & - 2172 \end{array}]$

有限数学 示例

有限数学示例