$$$\left[\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right]$$$ 的行列式
相关计算器: 代数余子式矩阵计算器
您的输入
计算 $$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right|$$$。
解答
2x2 矩阵的行列式为 $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$。
$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = \left(2 \cos{\left(5 v \right)}\right)\cdot \left(10 \cos{\left(5 v \right)}\right) - \left(- 10 u \sin{\left(5 v \right)}\right)\cdot \left(0\right) = 20 \cos^{2}{\left(5 v \right)}$$$
答案
$$$\left|\begin{array}{cc}2 \cos{\left(5 v \right)} & - 10 u \sin{\left(5 v \right)}\\0 & 10 \cos{\left(5 v \right)}\end{array}\right| = 20 \cos^{2}{\left(5 v \right)}$$$A