线性代数示例

$[\begin{array}{c} 3 & - 6 & 21 \\ 0 & 42 & - 21 \\ 2 & 24 & 0 \\ 2 & 54 & - 15 \end{array}]$

解题步骤 1

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

$[\begin{array}{c} \frac{3}{3} & \frac{- 6}{3} & \frac{21}{3} \\ 0 & 42 & - 21 \\ 2 & 24 & 0 \\ 2 & 54 & - 15 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 42 & - 21 \\ 2 & 24 & 0 \\ 2 & 54 & - 15 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 42 & - 21 \\ 2 - 2 \cdot 1 & 24 - 2 \cdot - 2 & 0 - 2 \cdot 7 \\ 2 & 54 & - 15 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 42 & - 21 \\ 0 & 28 & - 14 \\ 2 & 54 & - 15 \end{array}]$

解题步骤 3

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

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解题步骤 3.1

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

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 42 & - 21 \\ 0 & 28 & - 14 \\ 2 - 2 \cdot 1 & 54 - 2 \cdot - 2 & - 15 - 2 \cdot 7 \end{array}]$

解题步骤 3.2

化简 $R_{4}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 42 & - 21 \\ 0 & 28 & - 14 \\ 0 & 58 & - 29 \end{array}]$

解题步骤 4

Multiply each element of $R_{2}$ by $\frac{1}{42}$ 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 $\frac{1}{42}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 2 & 7 \\ \frac{0}{42} & \frac{42}{42} & \frac{- 21}{42} \\ 0 & 28 & - 14 \\ 0 & 58 & - 29 \end{array}]$

解题步骤 4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 1 & - \frac{1}{2} \\ 0 & 28 & - 14 \\ 0 & 58 & - 29 \end{array}]$

解题步骤 5

Perform the row operation $R_{3} = R_{3} - 28 R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 5.1

Perform the row operation $R_{3} = R_{3} - 28 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 1 & - \frac{1}{2} \\ 0 - 28 \cdot 0 & 28 - 28 \cdot 1 & - 14 - 28 (- \frac{1}{2}) \\ 0 & 58 & - 29 \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 1 & - \frac{1}{2} \\ 0 & 0 & 0 \\ 0 & 58 & - 29 \end{array}]$

解题步骤 6

Perform the row operation $R_{4} = R_{4} - 58 R_{2}$ to make the entry at $4, 2$ a $0$ .

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解题步骤 6.1

Perform the row operation $R_{4} = R_{4} - 58 R_{2}$ to make the entry at $4, 2$ a $0$ .

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 1 & - \frac{1}{2} \\ 0 & 0 & 0 \\ 0 - 58 \cdot 0 & 58 - 58 \cdot 1 & - 29 - 58 (- \frac{1}{2}) \end{array}]$

解题步骤 6.2

化简 $R_{4}$ 。

$[\begin{array}{c} 1 & - 2 & 7 \\ 0 & 1 & - \frac{1}{2} \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}]$

解题步骤 7

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 7.1

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

$[\begin{array}{c} 1 + 2 \cdot 0 & - 2 + 2 \cdot 1 & 7 + 2 (- \frac{1}{2}) \\ 0 & 1 & - \frac{1}{2} \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}]$

解题步骤 7.2

化简 $R_{1}$ 。

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

线性代数 示例

线性代数示例