线性代数示例

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

解题步骤 1

Swap $R_{4}$ with $R_{1}$ to put a nonzero entry at $1, 2$ .

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

解题步骤 2

Swap $R_{3}$ with $R_{2}$ to put a nonzero entry at $2, 3$ .

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

解题步骤 3

Perform the row operation $R_{2} = R_{2} - R_{4}$ to make the entry at $2, 5$ a $0$ .

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解题步骤 3.1

Perform the row operation $R_{2} = R_{2} - R_{4}$ to make the entry at $2, 5$ a $0$ .

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

解题步骤 3.2

化简 $R_{2}$ 。

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

解题步骤 4

Perform the row operation $R_{1} = R_{1} - R_{4}$ to make the entry at $1, 5$ a $0$ .

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解题步骤 4.1

Perform the row operation $R_{1} = R_{1} - R_{4}$ to make the entry at $1, 5$ a $0$ .

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

解题步骤 4.2

化简 $R_{1}$ 。

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

解题步骤 5

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

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解题步骤 5.1

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

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

解题步骤 5.2

化简 $R_{1}$ 。

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

线性代数 示例

线性代数示例