Algèbre Exemples

$[\begin{array}{c} - 6 & 7 & 8 & 0 \\ 0 & 6 & 13 & 7 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $- \frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

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Multiply each element of $R_{1}$ by $- \frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{6} \cdot - 6 & - \frac{1}{6} \cdot 7 & - \frac{1}{6} \cdot 8 & - \frac{1}{6} \cdot 0 \\ 0 & 6 & 13 & 7 \end{array}]$

Simplifiez $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{7}{6} & - \frac{4}{3} & 0 \\ 0 & 6 & 13 & 7 \end{array}]$

Step 2

Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

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Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{7}{6} & - \frac{4}{3} & 0 \\ \frac{0}{6} & \frac{6}{6} & \frac{13}{6} & \frac{7}{6} \end{array}]$

Simplifiez $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{7}{6} & - \frac{4}{3} & 0 \\ 0 & 1 & \frac{13}{6} & \frac{7}{6} \end{array}]$

Step 3

Perform the row operation $R_{1} = R_{1} + \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Perform the row operation $R_{1} = R_{1} + \frac{7}{6} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + \frac{7}{6} \cdot 0 & - \frac{7}{6} + \frac{7}{6} \cdot 1 & - \frac{4}{3} + \frac{7}{6} \cdot \frac{13}{6} & 0 + \frac{7}{6} \cdot \frac{7}{6} \\ 0 & 1 & \frac{13}{6} & \frac{7}{6} \end{array}]$

Simplifiez $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{43}{36} & \frac{49}{36} \\ 0 & 1 & \frac{13}{6} & \frac{7}{6} \end{array}]$