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

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

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

$$$\left|\begin{array}{cc}3 - \lambda & -4\\1 & 3 - \lambda\end{array}\right| = \left(3 - \lambda\right)\cdot \left(3 - \lambda\right) - \left(-4\right)\cdot \left(1\right) = \lambda^{2} - 6 \lambda + 13$$$

$$$\left|\begin{array}{cc}3 - \lambda & -4\\1 & 3 - \lambda\end{array}\right| = \lambda^{2} - 6 \lambda + 13$$$A