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First I have to find the eigenvalues and vectors for

[a 0 1]

[0 b 0]

[0 0 c] where a =/= b =/= c.

I looked around online and could only find that the answers for the eigenvalues are a, b, and c but I have no idea how that answer is derived. And I have no idea how to solve for eigenvectors except so any help would be great.

Next I have to do the same thing for

[a a 0]

[2a 0 0]

[0 a a] where a =/= 0.

Again I know that the solution for the values is -a, a, and 2a but no clue on how to actually do the problem.

I know nothing of this material except how to figure out the determinant of a matrix. So detailed steps on how to solve for eigenvalues and eigenvectors would be greatly appreciated.