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$[\begin{array}{c} 3 & 0 & 9 \\ - 2 & 4 & 12 \end{array}]$

Bước 1

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

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Bước 1.1

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

$[\begin{array}{c} \frac{3}{3} & \frac{0}{3} & \frac{9}{3} \\ - 2 & 4 & 12 \end{array}]$

Bước 1.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 3 \\ - 2 & 4 & 12 \end{array}]$

Bước 2

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

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Bước 2.1

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

$[\begin{array}{c} 1 & 0 & 3 \\ - 2 + 2 \cdot 1 & 4 + 2 \cdot 0 & 12 + 2 \cdot 3 \end{array}]$

Bước 2.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 0 & 3 \\ 0 & 4 & 18 \end{array}]$

Bước 3

Multiply each element of $R_{2}$ by $\frac{1}{4}$ to make the entry at $2, 2$ a $1$ .

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Bước 3.1

Multiply each element of $R_{2}$ by $\frac{1}{4}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & 3 \\ \frac{0}{4} & \frac{4}{4} & \frac{18}{4} \end{array}]$

Bước 3.2

Rút gọn $R_{2}$ .

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