I think you have no other choice than finding the characteristic polynomial and the eigenvalues.
Then find k such that at least one of the eigenspaces has a dimension < to the order of multiplicity of the eigenvalue...
Hi my question is
Find all the values of k for which the matrix
0, 1, 0
0, 0, 1
0, -k-2, k+3
is not diagonalizable over C. i understand how to diagonlize matrices but i do
not understand what values of k make the above statement true.