$$$\left[\begin{array}{cc}\frac{4}{5} - \lambda & \frac{3}{10}\\\frac{1}{5} & \frac{7}{10} - \lambda\end{array}\right]$$$ 的行列式
相關計算器: 代數餘子式矩陣計算器
您的輸入
計算 $$$\left|\begin{array}{cc}\frac{4}{5} - \lambda & \frac{3}{10}\\\frac{1}{5} & \frac{7}{10} - \lambda\end{array}\right|$$$。
解答
2x2 矩陣的行列式為 $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$。
$$$\left|\begin{array}{cc}\frac{4}{5} - \lambda & \frac{3}{10}\\\frac{1}{5} & \frac{7}{10} - \lambda\end{array}\right| = \left(\frac{4}{5} - \lambda\right)\cdot \left(\frac{7}{10} - \lambda\right) - \left(\frac{3}{10}\right)\cdot \left(\frac{1}{5}\right) = \lambda^{2} - \frac{3 \lambda}{2} + \frac{1}{2}$$$
答案
$$$\left|\begin{array}{cc}\frac{4}{5} - \lambda & \frac{3}{10}\\\frac{1}{5} & \frac{7}{10} - \lambda\end{array}\right| = \frac{\left(\lambda - 1\right) \left(2 \lambda - 1\right)}{2} = 0.5 \left(\lambda - 1\right) \left(2 \lambda - 1\right)$$$A