线性代数示例

$[\begin{array}{c} 0 & \cos (x) & \sin (x) \\ 0 & - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \\ 0 & 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array}]$

Step 1

Multiply every element in the $1 s t$ column by its cofactor and add.

$0 | \begin{array}{c} - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \\ 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array} | + 0 | \begin{array}{c} \cos (x) & \sin (x) \\ 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array} | + 0 | \begin{array}{c} \cos (x) & \sin (x) \\ - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \end{array} |$

Step 2

将 $0$ 乘以 $| \begin{array}{c} - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \\ 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array} |$ 。

$0 + 0 | \begin{array}{c} \cos (x) & \sin (x) \\ 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array} | + 0 | \begin{array}{c} \cos (x) & \sin (x) \\ - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \end{array} |$

Step 3

将 $0$ 乘以 $| \begin{array}{c} \cos (x) & \sin (x) \\ 3 \cos (x) + 4 \sin (x) & - 4 \cos (x) + 3 \sin (x) \end{array} |$ 。

$0 + 0 + 0 | \begin{array}{c} \cos (x) & \sin (x) \\ - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \end{array} |$

Step 4

将 $0$ 乘以 $| \begin{array}{c} \cos (x) & \sin (x) \\ - 2 \cos (x) - \sin (x) & \cos (x) - 2 \sin (x) \end{array} |$ 。

$0 + 0 + 0$

Step 5

化简行列式。

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将 $0$ 和 $0$ 相加。

$0 + 0$

将 $0$ 和 $0$ 相加。

$0$

线性代数 示例

线性代数示例