线性代数示例

$p = 2800$ , $i = 2 %$ , $n = 60$

解题步骤 1

将 $2 %$ 转换成一个小数。

$p = 2800, i = 0.02, n = 60$

解题步骤 2

从等式两边同时减去 $i$ 。

$p = 2800, 0 = 0.02 - i, n = 60$

解题步骤 3

以矩阵形式书写方程组。

$[\begin{array}{c} 0 & 1 & 2800 \\ 0 & 0 & 0.02 - i \\ 1 & 0 & 60 \end{array}]$

解题步骤 4

求行简化阶梯形矩阵。

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解题步骤 4.1

Swap $R_{3}$ with $R_{1}$ to put a nonzero entry at $1, 1$ .

$[\begin{array}{c} 1 & 0 & 60 \\ 0 & 0 & 0.02 - i \\ 0 & 1 & 2800 \end{array}]$

解题步骤 4.2

Swap $R_{3}$ with $R_{2}$ to put a nonzero entry at $2, 2$ .

$[\begin{array}{c} 1 & 0 & 60 \\ 0 & 1 & 2800 \\ 0 & 0 & 0.02 - i \end{array}]$

解题步骤 4.3

Multiply each element of $R_{3}$ by $\frac{1}{0.02 - i}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 4.3.1

Multiply each element of $R_{3}$ by $\frac{1}{0.02 - i}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & 60 \\ 0 & 1 & 2800 \\ \frac{0}{0.02 - i} & \frac{0}{0.02 - i} & \frac{0.02 - i}{0.02 - i} \end{array}]$

解题步骤 4.3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & 0 & 60 \\ 0 & 1 & 2800 \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.4

Perform the row operation $R_{2} = R_{2} - 2800 R_{3}$ to make the entry at $2, 3$ a $0$ .

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解题步骤 4.4.1

Perform the row operation $R_{2} = R_{2} - 2800 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & 60 \\ 0 - 2800 \cdot 0 & 1 - 2800 \cdot 0 & 2800 - 2800 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 0 & 60 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.5

Perform the row operation $R_{1} = R_{1} - 60 R_{3}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 4.5.1

Perform the row operation $R_{1} = R_{1} - 60 R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 60 \cdot 0 & 0 - 60 \cdot 0 & 60 - 60 \cdot 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

解题步骤 4.5.2

化简 $R_{1}$ 。

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

解题步骤 5

使用结果矩阵定义方程组的最终解。

$n = 0$

$p = 0$

$0 = 1$

解题步骤 6

因为 $0 \neq 1$ ，所以没有解。

无解

线性代数 示例

线性代数示例