线性代数示例

$y = 5 x - 1$ , $y = 5 x - 2$

解题步骤 1

从等式两边同时减去 $5 x$ 。

$y - 5 x = - 1, y = 5 x - 2$

解题步骤 2

从等式两边同时减去 $5 x$ 。

$y - 5 x = - 1, y - 5 x = - 2$

解题步骤 3

以矩阵形式书写方程组。

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

解题步骤 4

求行简化阶梯形矩阵。

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解题步骤 4.1

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

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解题步骤 4.1.1

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

$[\begin{array}{c} - \frac{1}{5} \cdot - 5 & - \frac{1}{5} \cdot 1 & - \frac{1}{5} \cdot - 1 \\ - 5 & 1 & - 2 \end{array}]$

解题步骤 4.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{1}{5} & \frac{1}{5} \\ - 5 & 1 & - 2 \end{array}]$

解题步骤 4.2

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

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解题步骤 4.2.1

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

$[\begin{array}{c} 1 & - \frac{1}{5} & \frac{1}{5} \\ - 5 + 5 \cdot 1 & 1 + 5 (- \frac{1}{5}) & - 2 + 5 (\frac{1}{5}) \end{array}]$

解题步骤 4.2.2

化简 $R_{2}$ 。

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

解题步骤 4.3

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

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解题步骤 4.3.1

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

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

解题步骤 4.3.2

化简 $R_{2}$ 。

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

解题步骤 4.4

Perform the row operation $R_{1} = R_{1} - \frac{1}{5} R_{2}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 4.4.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{5} R_{2}$ to make the entry at $1, 3$ a $0$ .

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

解题步骤 4.4.2

化简 $R_{1}$ 。

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

解题步骤 5

使用结果矩阵定义方程组的最终解。

$x - \frac{y}{5} = 0$

$0 = 1$

解题步骤 6

在等式两边都加上 $\frac{y}{5}$ 。

$x = \frac{y}{5}$

$0 = 1$

解题步骤 7

因为 $0 \neq 1$ ，所以没有解。

无解

线性代数 示例

线性代数示例