线性代数示例

$13 x - 6 y = 10$ , $26 x - 12 y = 15$

解题步骤 1

以矩阵形式书写方程组。

$[\begin{array}{c} 13 & - 6 & 10 \\ 26 & - 12 & 15 \end{array}]$

解题步骤 2

求行简化阶梯形矩阵。

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解题步骤 2.1

Multiply each element of $R_{1}$ by $\frac{1}{13}$ to make the entry at $1, 1$ a $1$ .

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解题步骤 2.1.1

Multiply each element of $R_{1}$ by $\frac{1}{13}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{13}{13} & \frac{- 6}{13} & \frac{10}{13} \\ 26 & - 12 & 15 \end{array}]$

解题步骤 2.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{6}{13} & \frac{10}{13} \\ 26 & - 12 & 15 \end{array}]$

解题步骤 2.2

Perform the row operation $R_{2} = R_{2} - 26 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 2.2.1

Perform the row operation $R_{2} = R_{2} - 26 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{6}{13} & \frac{10}{13} \\ 26 - 26 \cdot 1 & - 12 - 26 (- \frac{6}{13}) & 15 - 26 (\frac{10}{13}) \end{array}]$

解题步骤 2.2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{6}{13} & \frac{10}{13} \\ 0 & 0 & - 5 \end{array}]$

解题步骤 2.3

Multiply each element of $R_{2}$ by $- \frac{1}{5}$ to make the entry at $2, 3$ a $1$ .

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解题步骤 2.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{5}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{6}{13} & \frac{10}{13} \\ - \frac{1}{5} \cdot 0 & - \frac{1}{5} \cdot 0 & - \frac{1}{5} \cdot - 5 \end{array}]$

解题步骤 2.3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{6}{13} & \frac{10}{13} \\ 0 & 0 & 1 \end{array}]$

解题步骤 2.4

Perform the row operation $R_{1} = R_{1} - \frac{10}{13} R_{2}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{10}{13} R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - \frac{10}{13} \cdot 0 & - \frac{6}{13} - \frac{10}{13} \cdot 0 & \frac{10}{13} - \frac{10}{13} \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 2.4.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{6}{13} & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 3

使用结果矩阵定义方程组的最终解。

$x - \frac{6 y}{13} = 0$

$0 = 1$

解题步骤 4

在等式两边都加上 $\frac{6 y}{13}$ 。

$x = \frac{6 y}{13}$

$0 = 1$

解题步骤 5

因为 $0 \neq 1$ ，所以没有解。

无解

线性代数 示例

线性代数示例