Question

Find the characteristic polynomial of the matrix a=[−83−310].

Answer 1

Assuming the matrix is

$\mathbf A=\begin{bmatrix}-8&3\\-3&10\end{bmatrix}$

we have characteristic polynomial given by the equation

$\det(\mathbf A-\lambda \mathbf I)=0\iff\begin{vmatrix}-8-\lambda&3\\-3&10-\lambda\end{vmatrix}=0$
$(-8-\lambda)(10-\lambda)-(-9)=0$
$\lambda^2-2\lambda-71=0$