Eigenvector of 3x3 matrix with complex eigenvalues

[rayne1]

Matrix A:
0 -6 10
-2 12 -20
-1 6 -10

I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of:
1 0 0 | 0
0 1 0 | 0
0 0 1 | 0

So, how do I find the nonzero eigenvectors of the complex eigenvalues?

 

[I like Serena]

Matrix A:
0 -6 10
-2 12 -20
-1 6 -10

I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of:
1 0 0 | 0
0 1 0 | 0
0 0 1 | 0

So, how do I find the nonzero eigenvectors of the complex eigenvalues?

Hi rayne!

It means that 1+i and 1-i are not actually eigenvalues.
How did you conclude they were?