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Eigenvectors

Question: Find eigenvalues and normalised eigenvectors of following symmetric matrix:


10 0 6
0 2 0
6 0 -6

Worked out the eigenvalues which are: 2, -8, 12
I know these are correct.

However, quite stumped on how to find the vectors - my teacher just posts the answer with no explanation and previous notes are useless.

Can someone explain how to do them?

Ta
Reply 1
Avatar for DFranklin
DFranklin
18
Suppose A is your original matrix, and t is an eigenvalue.

Calculate the matrix A-tI, and then solve for a non trivial column vector v s.t. (A-tI)v = 0. (Here non-trivial means v can't equal the zero vector).

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