有限数学示例

$2 x + 6 y = 7$ , $- 3 x - 9 y = - 10$

解题步骤 1

Write the system as a matrix.

$[\begin{array}{c} 2 & 6 & 7 \\ - 3 & - 9 & - 10 \end{array}]$

解题步骤 2

求行简化阶梯形矩阵。

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解题步骤 2.1

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

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解题步骤 2.1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{6}{2} & \frac{7}{2} \\ - 3 & - 9 & - 10 \end{array}]$

解题步骤 2.1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 3 & \frac{7}{2} \\ - 3 & - 9 & - 10 \end{array}]$

解题步骤 2.2

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

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解题步骤 2.2.1

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

$[\begin{array}{c} 1 & 3 & \frac{7}{2} \\ - 3 + 3 \cdot 1 & - 9 + 3 \cdot 3 & - 10 + 3 (\frac{7}{2}) \end{array}]$

解题步骤 2.2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 3 & \frac{7}{2} \\ 0 & 0 & \frac{1}{2} \end{array}]$

解题步骤 2.3

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

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解题步骤 2.3.1

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

$[\begin{array}{c} 1 & 3 & \frac{7}{2} \\ 2 \cdot 0 & 2 \cdot 0 & 2 (\frac{1}{2}) \end{array}]$

解题步骤 2.3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & 3 & \frac{7}{2} \\ 0 & 0 & 1 \end{array}]$

解题步骤 2.4

Perform the row operation $R_{1} = R_{1} - \frac{7}{2} R_{2}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 2.4.1

Perform the row operation $R_{1} = R_{1} - \frac{7}{2} R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - \frac{7}{2} \cdot 0 & 3 - \frac{7}{2} \cdot 0 & \frac{7}{2} - \frac{7}{2} \cdot 1 \\ 0 & 0 & 1 \end{array}]$

解题步骤 2.4.2

化简 $R_{1}$ 。

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

解题步骤 3

Use the result matrix to declare the final solution to the system of equations.

$x + 3 y = 0$

$0 = 1$

解题步骤 4

The system is inconsistent so there is no solution.

$无解$

有限数学 示例

有限数学示例