Finding Eigenvectors for a Matrix A

[bluewhistled]

Homework Statement

a matrix A:
[1 3 0
3 1 0
0 0 -2]

Find Q and D where

Q^TAQ=D

The Attempt at a Solution

I found the eigenvalues of -4,2,2

When I plug them back in and rref the matrix I only get the trivial solution meaning the matrices are linearly independent. How do I get the eigenvectors if that's the case?

 

[Defennder]

Check your eigenvalues.

 

[bluewhistled]

[L-1 -3 0
-3 L-1 0
0 0 L+2]

(L+2)((L-1)^2 - 9)
(L+2)(L^2 -2L +1 -9)
(L+2)(L^2 -2L -8)
(L^3 -2L^2 -8L +2L^2 -4L -16)
L^3 -12L -16
...
meh, got it nevermind. Thanks for the suggestion.