Determine if the following matrix is diagonalizable.

A =
[
−4 0 0 0 0
4 2 0 0 0
−2 3 1 0 0
0 5 3 − 1 0
3 1 8 4 3 ]

Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.