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$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}]$

خطوة 1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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خطوة 1.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & 3 \\ 4 - 4 \cdot 1 & 5 - 4 \cdot 2 & 6 - 4 \cdot 3 \end{array}]$

خطوة 1.2

بسّط $R_{2}$ .

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \end{array}]$

خطوة 2

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

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خطوة 2.1

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

$[\begin{array}{c} 1 & 2 & 3 \\ - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 6 \end{array}]$

خطوة 2.2

بسّط $R_{2}$ .

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

خطوة 3

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

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خطوة 3.1

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

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

خطوة 3.2

بسّط $R_{1}$ .

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