The matrix A below has charachteristic polynomial (λ+1)2(λ-2)2. Compute bases for the(+2)eigenspace and the (-1)eigenspace and explain why A is not diagonalizable
As in your previous thread, solve for X in :
(definition of eigenvalue, that will give you eigenspaces for each eigenvalues)
So solve for X in -> (+2) eigenspace
-> (-1) eigenspace
If the dimension of the (+2) eigenspace plus the dimension of the (-1) eigenspace is inferior to 4, then the matrix is not diagonalizable.