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$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 2 & 4 & 6 & 8 \\ 3 & 6 & 9 & 12 \\ 4 & 8 & 12 & 16 \end{array}]$

Bước 1

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 1.1

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

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 2 - 2 \cdot 1 & 4 - 2 \cdot 2 & 6 - 2 \cdot 3 & 8 - 2 \cdot 4 \\ 3 & 6 & 9 & 12 \\ 4 & 8 & 12 & 16 \end{array}]$

Bước 1.2

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 0 \\ 3 & 6 & 9 & 12 \\ 4 & 8 & 12 & 16 \end{array}]$

Bước 2

Perform the row operation $R_{3} = R_{3} - 3 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Bước 2.1

Perform the row operation $R_{3} = R_{3} - 3 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 0 \\ 3 - 3 \cdot 1 & 6 - 3 \cdot 2 & 9 - 3 \cdot 3 & 12 - 3 \cdot 4 \\ 4 & 8 & 12 & 16 \end{array}]$

Bước 2.2

Rút gọn $R_{3}$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 4 & 8 & 12 & 16 \end{array}]$

Bước 3

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

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Bước 3.1

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

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 4 - 4 \cdot 1 & 8 - 4 \cdot 2 & 12 - 4 \cdot 3 & 16 - 4 \cdot 4 \end{array}]$

Bước 3.2

Rút gọn $R_{4}$ .

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