线性代数示例

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 4 & 5 & 6 & 7 \\ 6 & 7 & 8 & 9 \end{array}]$

解题步骤 1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 1.1

Perform the row operation $R_{2} = R_{2} - 4 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 4 - 4 \cdot 1 & 5 - 4 \cdot 2 & 6 - 4 \cdot 3 & 7 - 4 \cdot 4 \\ 6 & 7 & 8 & 9 \end{array}]$

解题步骤 1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & - 3 & - 6 & - 9 \\ 6 & 7 & 8 & 9 \end{array}]$

解题步骤 2

Perform the row operation $R_{3} = R_{3} - 6 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{3} = R_{3} - 6 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & - 3 & - 6 & - 9 \\ 6 - 6 \cdot 1 & 7 - 6 \cdot 2 & 8 - 6 \cdot 3 & 9 - 6 \cdot 4 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & - 3 & - 6 & - 9 \\ 0 & - 5 & - 10 & - 15 \end{array}]$

解题步骤 3

Multiply each element of $R_{2}$ by $- \frac{1}{3}$ 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 $- \frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 6 & - \frac{1}{3} \cdot - 9 \\ 0 & - 5 & - 10 & - 15 \end{array}]$

解题步骤 3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & - 5 & - 10 & - 15 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 + 5 \cdot 0 & - 5 + 5 \cdot 1 & - 10 + 5 \cdot 2 & - 15 + 5 \cdot 3 \end{array}]$

解题步骤 4.2

化简 $R_{3}$ 。

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

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 $0$ .

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

解题步骤 5.2

化简 $R_{1}$ 。

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

线性代数 示例

线性代数示例