线性代数示例

$y = - 2 - 3$ , $y = 1$

解题步骤 1

从 $- 2$ 中减去 $3$ 。

$y = - 5, y = 1$

解题步骤 2

以矩阵形式书写方程组。

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

解题步骤 3

求行简化阶梯形矩阵。

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解题步骤 3.1

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

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解题步骤 3.1.1

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

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

解题步骤 3.1.2

化简 $R_{2}$ 。

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

解题步骤 3.2

Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 3.2.1

Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

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

解题步骤 3.2.2

化简 $R_{2}$ 。

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

解题步骤 3.3

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

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解题步骤 3.3.1

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

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

解题步骤 3.3.2

化简 $R_{1}$ 。

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

解题步骤 4

使用结果矩阵定义方程组的最终解。

$y = 0$

$0 = 1$

解题步骤 5

因为 $0 \neq 1$ ，所以没有解。

无解

线性代数 示例