线性代数示例

$288 = 75 x + 85 x$ , $288 = 100 x$

解题步骤 1

将 $75 x$ 和 $85 x$ 相加。

$288 = 160 x, 288 = 100 x$

解题步骤 2

从等式两边同时减去 $288$ 。

$0 = 160 x - 288, 288 = 100 x$

解题步骤 3

从等式两边同时减去 $160 x$ 。

$- 160 x = - 288, 288 = 100 x$

解题步骤 4

从等式两边同时减去 $288$ 。

$- 160 x = - 288, 0 = 100 x - 288$

解题步骤 5

从等式两边同时减去 $100 x$ 。

$- 160 x = - 288, - 100 x = - 288$

解题步骤 6

以矩阵形式书写方程组。

$[\begin{array}{c} - 160 & - 288 \\ - 100 & - 288 \end{array}]$

解题步骤 7

求行简化阶梯形矩阵。

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解题步骤 7.1

Multiply each element of $R_{1}$ by $- \frac{1}{160}$ to make the entry at $1, 1$ a $1$ .

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解题步骤 7.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{160}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{160} \cdot - 160 & - \frac{1}{160} \cdot - 288 \\ - 100 & - 288 \end{array}]$

解题步骤 7.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & \frac{9}{5} \\ - 100 & - 288 \end{array}]$

解题步骤 7.2

Perform the row operation $R_{2} = R_{2} + 100 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 7.2.1

Perform the row operation $R_{2} = R_{2} + 100 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{9}{5} \\ - 100 + 100 \cdot 1 & - 288 + 100 (\frac{9}{5}) \end{array}]$

解题步骤 7.2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & \frac{9}{5} \\ 0 & - 108 \end{array}]$

解题步骤 7.3

Multiply each element of $R_{2}$ by $- \frac{1}{108}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 7.3.1

Multiply each element of $R_{2}$ by $- \frac{1}{108}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{9}{5} \\ - \frac{1}{108} \cdot 0 & - \frac{1}{108} \cdot - 108 \end{array}]$

解题步骤 7.3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & \frac{9}{5} \\ 0 & 1 \end{array}]$

解题步骤 7.4

Perform the row operation $R_{1} = R_{1} - \frac{9}{5} R_{2}$ to make the entry at $1, 2$ a $0$ .

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解题步骤 7.4.1

Perform the row operation $R_{1} = R_{1} - \frac{9}{5} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{9}{5} \cdot 0 & \frac{9}{5} - \frac{9}{5} \cdot 1 \\ 0 & 1 \end{array}]$

解题步骤 7.4.2

化简 $R_{1}$ 。

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

解题步骤 8

使用结果矩阵定义方程组的最终解。

$x = 0$

$0 = 1$

解题步骤 9

因为 $0 \neq 1$ ，所以没有解。

无解

线性代数 示例

线性代数示例