Đại số Ví dụ

$[\begin{array}{c} 1 & 1 & 1 & 28 \\ 6000 & 12000 & 24000 & 420000 \end{array}]$

Step 1

Perform the row operation $R_{2} = R_{2} - 6000 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Perform the row operation $R_{2} = R_{2} - 6000 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 1 & 28 \\ 6000 - 6000 \cdot 1 & 12000 - 6000 \cdot 1 & 24000 - 6000 \cdot 1 & 420000 - 6000 \cdot 28 \end{array}]$

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 28 \\ 0 & 6000 & 18000 & 252000 \end{array}]$

Step 2

Multiply each element of $R_{2}$ by $\frac{1}{6000}$ to make the entry at $2, 2$ a $1$ .

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Multiply each element of $R_{2}$ by $\frac{1}{6000}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 1 & 1 & 28 \\ \frac{1}{6000} \cdot 0 & \frac{1}{6000} \cdot 6000 & \frac{1}{6000} \cdot 18000 & \frac{1}{6000} \cdot 252000 \end{array}]$

Rút gọn $R_{2}$ .

$[\begin{array}{c} 1 & 1 & 1 & 28 \\ 0 & 1 & 3 & 42 \end{array}]$

Step 3

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

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 1 - 3 & 28 - 42 \\ 0 & 1 & 3 & 42 \end{array}]$

Rút gọn $R_{1}$ .

$[\begin{array}{c} 1 & 0 & - 2 & - 14 \\ 0 & 1 & 3 & 42 \end{array}]$