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$[\begin{array}{c} 2 & 5 & 27 & 29 \\ 10 & 26 & 141 & 149 \end{array}]$

Bước 1

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

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Bước 1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{5}{2} & \frac{27}{2} & \frac{29}{2} \\ 10 & 26 & 141 & 149 \end{array}]$

Bước 1.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{27}{2} & \frac{29}{2} \\ 10 & 26 & 141 & 149 \end{array}]$

Bước 2

Perform the row operation $R_{2} = R_{2} - 10 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Bước 2.1

Perform the row operation $R_{2} = R_{2} - 10 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{27}{2} & \frac{29}{2} \\ 10 - 10 \cdot 1 & 26 - 10 (\frac{5}{2}) & 141 - 10 (\frac{27}{2}) & 149 - 10 (\frac{29}{2}) \end{array}]$

Bước 2.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{27}{2} & \frac{29}{2} \\ 0 & 1 & 6 & 4 \end{array}]$

Bước 3

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Bước 3.1

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{5}{2} \cdot 0 & \frac{5}{2} - \frac{5}{2} \cdot 1 & \frac{27}{2} - \frac{5}{2} \cdot 6 & \frac{29}{2} - \frac{5}{2} \cdot 4 \\ 0 & 1 & 6 & 4 \end{array}]$

Bước 3.2

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - \frac{3}{2} & \frac{9}{2} \\ 0 & 1 & 6 & 4 \end{array}]$