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For which values of a is the following matrix not diagonalizable?

... 4 0 6

A = ( 2 a 3 )

...-1 0 -1

So my first question is when is a matrix diagonalizable or not diafonalizable.

The way I approached the question was to go about finding the eigenvalues and eigenvectors.

p(h) = (4-h)(a-h)(-1-h)-(-1)(a-h)(6)

Distributing this out gets pretty messy. So it doesn't seem like this is the right approach.

Can someone help me out please? How do I go about solving this?