线性代数示例

$[\begin{array}{c} 6 & 3 & 3 & 33 \\ 3 & 3 & 0 & 15 \\ 3 & 0 & 3 & 18 \end{array}]$

解题步骤 1

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

$[\begin{array}{c} \frac{6}{6} & \frac{3}{6} & \frac{3}{6} & \frac{33}{6} \\ 3 & 3 & 0 & 15 \\ 3 & 0 & 3 & 18 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 3 & 3 & 0 & 15 \\ 3 & 0 & 3 & 18 \end{array}]$

解题步骤 2

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

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解题步骤 2.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 3 - 3 \cdot 1 & 3 - 3 (\frac{1}{2}) & 0 - 3 (\frac{1}{2}) & 15 - 3 (\frac{11}{2}) \\ 3 & 0 & 3 & 18 \end{array}]$

解题步骤 2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 0 & \frac{3}{2} & - \frac{3}{2} & - \frac{3}{2} \\ 3 & 0 & 3 & 18 \end{array}]$

解题步骤 3

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

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解题步骤 3.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 0 & \frac{3}{2} & - \frac{3}{2} & - \frac{3}{2} \\ 3 - 3 \cdot 1 & 0 - 3 (\frac{1}{2}) & 3 - 3 (\frac{1}{2}) & 18 - 3 (\frac{11}{2}) \end{array}]$

解题步骤 3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 0 & \frac{3}{2} & - \frac{3}{2} & - \frac{3}{2} \\ 0 & - \frac{3}{2} & \frac{3}{2} & \frac{3}{2} \end{array}]$

解题步骤 4

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

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解题步骤 4.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ \frac{2}{3} \cdot 0 & \frac{2}{3} \cdot \frac{3}{2} & \frac{2}{3} (- \frac{3}{2}) & \frac{2}{3} (- \frac{3}{2}) \\ 0 & - \frac{3}{2} & \frac{3}{2} & \frac{3}{2} \end{array}]$

解题步骤 4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 0 & 1 & - 1 & - 1 \\ 0 & - \frac{3}{2} & \frac{3}{2} & \frac{3}{2} \end{array}]$

解题步骤 5

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

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解题步骤 5.1

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

$[\begin{array}{c} 1 & \frac{1}{2} & \frac{1}{2} & \frac{11}{2} \\ 0 & 1 & - 1 & - 1 \\ 0 + \frac{3}{2} \cdot 0 & - \frac{3}{2} + \frac{3}{2} \cdot 1 & \frac{3}{2} + \frac{3}{2} \cdot - 1 & \frac{3}{2} + \frac{3}{2} \cdot - 1 \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

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

解题步骤 6

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

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解题步骤 6.1

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

$[\begin{array}{c} 1 - \frac{1}{2} \cdot 0 & \frac{1}{2} - \frac{1}{2} \cdot 1 & \frac{1}{2} - \frac{1}{2} \cdot - 1 & \frac{11}{2} - \frac{1}{2} \cdot - 1 \\ 0 & 1 & - 1 & - 1 \\ 0 & 0 & 0 & 0 \end{array}]$

解题步骤 6.2

化简 $R_{1}$ 。

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

线性代数 示例

线性代数示例