Determinant of $\left[\begin{array}{cc}3 - \lambda & -10\\1 & - \lambda - 4\end{array}\right]$

Calculate $\left|\begin{array}{cc}3 - \lambda & -10\\1 & - \lambda - 4\end{array}\right|$.

The determinant of a 2x2 matrix is $\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$.

$\left|\begin{array}{cc}3 - \lambda & -10\\1 & - \lambda - 4\end{array}\right| = \left(3 - \lambda\right)\cdot \left(- \lambda - 4\right) - \left(-10\right)\cdot \left(1\right) = \lambda^{2} + \lambda - 2$

$\left|\begin{array}{cc}3 - \lambda & -10\\1 & - \lambda - 4\end{array}\right| = \left(\lambda - 1\right) \left(\lambda + 2\right)$A