线性代数示例

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

解题步骤 1

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

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解题步骤 1.1

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

$[\begin{array}{c} 1 & 5 & - 6 \\ 1 - 1 & 6 - 5 & 5 + 6 \\ 2 & 8 & 7 \end{array}]$

解题步骤 1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 2 & 8 & 7 \end{array}]$

解题步骤 2

Perform the row operation $R_{3} = R_{3} - 2 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{3} = R_{3} - 2 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 2 - 2 \cdot 1 & 8 - 2 \cdot 5 & 7 - 2 \cdot - 6 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 0 & - 2 & 19 \end{array}]$

解题步骤 3

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

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解题步骤 3.1

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

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 0 + 2 \cdot 0 & - 2 + 2 \cdot 1 & 19 + 2 \cdot 11 \end{array}]$

解题步骤 3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 0 & 0 & 41 \end{array}]$

解题步骤 4

Multiply each element of $R_{3}$ by $\frac{1}{41}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 4.1

Multiply each element of $R_{3}$ by $\frac{1}{41}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ \frac{0}{41} & \frac{0}{41} & \frac{41}{41} \end{array}]$

解题步骤 4.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 11 \\ 0 & 0 & 1 \end{array}]$

解题步骤 5

Perform the row operation $R_{2} = R_{2} - 11 R_{3}$ to make the entry at $2, 3$ a $0$ .

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解题步骤 5.1

Perform the row operation $R_{2} = R_{2} - 11 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 - 11 \cdot 0 & 1 - 11 \cdot 0 & 11 - 11 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 5.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 5 & - 6 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 6

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

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解题步骤 6.1

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

$[\begin{array}{c} 1 + 6 \cdot 0 & 5 + 6 \cdot 0 & - 6 + 6 \cdot 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 6.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 5 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 7

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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解题步骤 7.1

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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

解题步骤 7.2

化简 $R_{1}$ 。

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

线性代数 示例

线性代数示例