$$$\left[\begin{array}{cc}5 - \lambda & -4\\-4 & 5 - \lambda\end{array}\right]$$$ 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 $$$\left|\begin{array}{cc}5 - \lambda & -4\\-4 & 5 - \lambda\end{array}\right|$$$。
解答
2x2 矩阵的行列式为 $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$。
$$$\left|\begin{array}{cc}5 - \lambda & -4\\-4 & 5 - \lambda\end{array}\right| = \left(5 - \lambda\right)\cdot \left(5 - \lambda\right) - \left(-4\right)\cdot \left(-4\right) = \lambda^{2} - 10 \lambda + 9$$$
答案
$$$\left|\begin{array}{cc}5 - \lambda & -4\\-4 & 5 - \lambda\end{array}\right| = \left(\lambda - 9\right) \left(\lambda - 1\right)$$$A