Determinanten av $$$\left[\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right]$$$

Beräkna $$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right|$$$.

Determinanten för en 2x2-matris är $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \left(2 - \lambda\right)\cdot \left(5 - \lambda\right) - \left(1\right)\cdot \left(5\right) = \lambda^{2} - 7 \lambda + 5$$$

$$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \lambda^{2} - 7 \lambda + 5$$$A