Pregunta: Diagonalize the matrix A=[[5,0,0,0],[0,5,0,0],[1,4,-3,0],[-1,-2,0,-3]] if possible.

Given matrix $\begin{array}{c}\mathrm{A}=\left[\begin{array}{cccc}5& 0& 0& 0\\ 0& 5& 0& 0\\ 1& 4& -3& 0\\ -1& -2& 0& -3\end{array}\right]\end{array}$.

Set up the formula to find the characteristic equation $\mathrm{p}\left(\lambda \right)$.

$\mathrm{p}\left(\lambda \right)=\mathrm{d}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{t}(\mathrm{A}-\lambda {\mathrm{I}}_4)$