Algèbre Exemples

$A = [\begin{array}{c} 2 & - 2 & 9 \\ 1 & 2 & 3 \end{array}]$

Step 1

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

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Step 1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{- 2}{2} & \frac{9}{2} \\ 1 & 2 & 3 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & - 1 & \frac{9}{2} \\ 1 & 2 & 3 \end{array}]$

Step 2

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

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Step 2.1

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

$[\begin{array}{c} 1 & - 1 & \frac{9}{2} \\ 1 - 1 & 2 + 1 & 3 - \frac{9}{2} \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - 1 & \frac{9}{2} \\ 0 & 3 & - \frac{3}{2} \end{array}]$

Step 3

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

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Step 3.1

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 1 & \frac{9}{2} \\ \frac{0}{3} & \frac{3}{3} & \frac{- \frac{3}{2}}{3} \end{array}]$

Step 3.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - 1 & \frac{9}{2} \\ 0 & 1 & - \frac{1}{2} \end{array}]$

Step 4

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

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Step 4.1

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

$[\begin{array}{c} 1 + 0 & - 1 + 1 \cdot 1 & \frac{9}{2} - \frac{1}{2} \\ 0 & 1 & - \frac{1}{2} \end{array}]$

Step 4.2

Simplify $R_{1}$ .

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

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