Question

Find all the values of k for which the matrix
is not diagonizable over C
0 1 0
0 0 1
0 k-1 -k+2

Answer 1

do you have any idea?

Answer 2

well i know you find the characteristic equation but not sure where to go from there

Answer 3

it took me a long way to get the answer, so I am not sure whether mine is right or wrong,
just give you my idea. the condition for a matrix cannot be diagonized is it has a linear dependent eigenvectors

Answer 4

make up characteristic equation , solve for eigenvalues and then eigenvectors corresponding to those eigenvalues and make them linear dependent. that the condition for NOT get diagonalized matrix P which can diagonal A

Answer 5

hope this helps.

Answer 6

let hear other opinion, @Mertsj

Answer 7

I don't know this one.

Answer 8

@e.mccormick

Answer 9

@satellite73