Algèbre Exemples

$[\begin{array}{c} 6 & 12 & 16 \\ 18 & 7 & 10 \end{array}]$

Étape 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 $1$ .

$[\begin{array}{c} \frac{6}{6} & \frac{12}{6} & \frac{16}{6} \\ 18 & 7 & 10 \end{array}]$

Simplifiez $R_{1}$ .

$[\begin{array}{c} 1 & 2 & \frac{8}{3} \\ 18 & 7 & 10 \end{array}]$

Étape 2

Perform the row operation $R_{2} = R_{2} - 18 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Perform the row operation $R_{2} = R_{2} - 18 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & \frac{8}{3} \\ 18 - 18 \cdot 1 & 7 - 18 \cdot 2 & 10 - 18 (\frac{8}{3}) \end{array}]$

Simplifiez $R_{2}$ .

$[\begin{array}{c} 1 & 2 & \frac{8}{3} \\ 0 & - 29 & - 38 \end{array}]$

Étape 3

Multiply each element of $R_{2}$ by $- \frac{1}{29}$ to make the entry at $2, 2$ a $1$ .

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Multiply each element of $R_{2}$ by $- \frac{1}{29}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 2 & \frac{8}{3} \\ - \frac{1}{29} \cdot 0 & - \frac{1}{29} \cdot - 29 & - \frac{1}{29} \cdot - 38 \end{array}]$

Simplifiez $R_{2}$ .

$[\begin{array}{c} 1 & 2 & \frac{8}{3} \\ 0 & 1 & \frac{38}{29} \end{array}]$

Étape 4

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

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

$[\begin{array}{c} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & \frac{8}{3} - 2 (\frac{38}{29}) \\ 0 & 1 & \frac{38}{29} \end{array}]$

Simplifiez $R_{1}$ .

$[\begin{array}{c} 1 & 0 & \frac{4}{87} \\ 0 & 1 & \frac{38}{29} \end{array}]$