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

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

Wyznacznikiem macierzy 2x2 jest $\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$.

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

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