线性代数示例

$y = 4 x + 3$ , $y = 4 x - 4$

解题步骤 1

从等式两边同时减去 $4 x$ 。

$y - 4 x = 3, y = 4 x - 4$

解题步骤 2

从等式两边同时减去 $4 x$ 。

$y - 4 x = 3, y - 4 x = - 4$

解题步骤 3

以矩阵形式书写方程组。

$[\begin{array}{c} - 4 & 1 & 3 \\ - 4 & 1 & - 4 \end{array}]$

解题步骤 4

求行简化阶梯形矩阵。

点击获取更多步骤...

解题步骤 4.1

Multiply each element of $R_{1}$ by $- \frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

点击获取更多步骤...

解题步骤 4.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{4}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot 1 & - \frac{1}{4} \cdot 3 \\ - 4 & 1 & - 4 \end{array}]$

解题步骤 4.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{1}{4} & - \frac{3}{4} \\ - 4 & 1 & - 4 \end{array}]$

解题步骤 4.2

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

点击获取更多步骤...

解题步骤 4.2.1

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

$[\begin{array}{c} 1 & - \frac{1}{4} & - \frac{3}{4} \\ - 4 + 4 \cdot 1 & 1 + 4 (- \frac{1}{4}) & - 4 + 4 (- \frac{3}{4}) \end{array}]$

解题步骤 4.2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{1}{4} & - \frac{3}{4} \\ 0 & 0 & - 7 \end{array}]$

解题步骤 4.3

Multiply each element of $R_{2}$ by $- \frac{1}{7}$ to make the entry at $2, 3$ a $1$ .

点击获取更多步骤...

解题步骤 4.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{7}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{1}{4} & - \frac{3}{4} \\ - \frac{1}{7} \cdot 0 & - \frac{1}{7} \cdot 0 & - \frac{1}{7} \cdot - 7 \end{array}]$

解题步骤 4.3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{1}{4} & - \frac{3}{4} \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.4

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{2}$ to make the entry at $1, 3$ a $0$ .

点击获取更多步骤...

解题步骤 4.4.1

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + \frac{3}{4} \cdot 0 & - \frac{1}{4} + \frac{3}{4} \cdot 0 & - \frac{3}{4} + \frac{3}{4} \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.4.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{1}{4} & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 5

使用结果矩阵定义方程组的最终解。

$x - \frac{y}{4} = 0$

$0 = 1$

解题步骤 6

在等式两边都加上 $\frac{y}{4}$ 。

$x = \frac{y}{4}$

$0 = 1$

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