Let A$=$

$$

$4001$

$0132$

$0010$

$0001$

$.$

$($a$)$ Determine the eigenvalues of A$.$ use mu instead of lambda

$($b$)$ Determine the eigenvectors corresponding to each of the eigenvalues you found in

part $($a$).$ use c as variable

$($c$)$ Is A diagonalizable? If so$,$ find D and P so that D$=$ P$1$AP$.$