Determinante von $$$\left[\begin{array}{cc}1 - \lambda & 2\\3 & 4 - \lambda\end{array}\right]$$$

Berechne $$$\left|\begin{array}{cc}1 - \lambda & 2\\3 & 4 - \lambda\end{array}\right|$$$.

Die Determinante einer 2x2-Matrix ist $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}1 - \lambda & 2\\3 & 4 - \lambda\end{array}\right| = \left(1 - \lambda\right)\cdot \left(4 - \lambda\right) - \left(2\right)\cdot \left(3\right) = \lambda^{2} - 5 \lambda - 2$$$

$$$\left|\begin{array}{cc}1 - \lambda & 2\\3 & 4 - \lambda\end{array}\right| = \lambda^{2} - 5 \lambda - 2$$$A