线性代数示例

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

解题步骤 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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解题步骤 1.1

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

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

解题步骤 1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & - 3 \\ 0 & - 5 & 10 \\ 4 & 3 & - 2 \end{array}]$

解题步骤 2

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & - 3 \\ 0 & - 5 & 10 \\ 4 - 4 \cdot 1 & 3 - 4 \cdot 2 & - 2 - 4 \cdot - 3 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 2 & - 3 \\ 0 & - 5 & 10 \\ 0 & - 5 & 10 \end{array}]$

解题步骤 3

Multiply each element of $R_{2}$ by $- \frac{1}{5}$ 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 $- \frac{1}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 2 & - 3 \\ - \frac{1}{5} \cdot 0 & - \frac{1}{5} \cdot - 5 & - \frac{1}{5} \cdot 10 \\ 0 & - 5 & 10 \end{array}]$

解题步骤 3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & - 3 \\ 0 & 1 & - 2 \\ 0 & - 5 & 10 \end{array}]$

解题步骤 4

Perform the row operation $R_{3} = R_{3} + 5 R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 4.1

Perform the row operation $R_{3} = R_{3} + 5 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 2 & - 3 \\ 0 & 1 & - 2 \\ 0 + 5 \cdot 0 & - 5 + 5 \cdot 1 & 10 + 5 \cdot - 2 \end{array}]$

解题步骤 4.2

化简 $R_{3}$ 。

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

解题步骤 5

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 5.1

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

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

解题步骤 5.2

化简 $R_{1}$ 。

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

线性代数 示例