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`