$$$\left[\begin{array}{cc}\frac{2}{3} - \lambda & 0\\0 & \frac{1}{3} - \lambda\end{array}\right]$$$:n determinantti

Laske $$$\left|\begin{array}{cc}\frac{2}{3} - \lambda & 0\\0 & \frac{1}{3} - \lambda\end{array}\right|$$$.

2x2-matriisin determinantti on $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}\frac{2}{3} - \lambda & 0\\0 & \frac{1}{3} - \lambda\end{array}\right| = \left(\frac{2}{3} - \lambda\right)\cdot \left(\frac{1}{3} - \lambda\right) - \left(0\right)\cdot \left(0\right) = \lambda^{2} - \lambda + \frac{2}{9}$$$

$$$\left|\begin{array}{cc}\frac{2}{3} - \lambda & 0\\0 & \frac{1}{3} - \lambda\end{array}\right| = \lambda^{2} - \lambda + \frac{2}{9}\approx \lambda^{2} - \lambda + 0.222222222222222$$$A