线性代数示例

$[\begin{array}{c} - 1 & 2 & 4 \\ - 6 & 6 & 24 \end{array}]$

解题步骤 1

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

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解题步骤 1.1

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

$[\begin{array}{c} - - 1 & - 1 \cdot 2 & - 1 \cdot 4 \\ - 6 & 6 & 24 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - 2 & - 4 \\ - 6 & 6 & 24 \end{array}]$

解题步骤 2

Perform the row operation $R_{2} = R_{2} + 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{2} = R_{2} + 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - 2 & - 4 \\ - 6 + 6 \cdot 1 & 6 + 6 \cdot - 2 & 24 + 6 \cdot - 4 \end{array}]$

解题步骤 2.2

化简 $R_{2}$ 。

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

解题步骤 3

Multiply each element of $R_{2}$ by $- \frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 3.1

Multiply each element of $R_{2}$ by $- \frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

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

解题步骤 3.2

化简 $R_{2}$ 。

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

解题步骤 4

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

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解题步骤 4.1

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

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

解题步骤 4.2

化简 $R_{1}$ 。

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

线性代数 示例