Why Can't I Find All Eigenvectors for My 3x3 Matrix?

[haz]

Hey everyone.
I have a matrix A = {{7,-5,0},{-5,7,0},{0,0,-6}}
I have found the Eigenvalues, 2,12,-6 but I'm only getting one Eigenvector, (0,0,1)..
I know there is 2 others (-1,1,0) and (1,1,0) but I am unable to get them by hand.
Once I get the matrix in the form (A-λI)*v = o, I just get the one vector..
Any help is much appreciated.

 

[UltrafastPED]

Try this tutorial: "Eigenvectors and eigenspaces for a 3x3 matrix"
https://www.khanacademy.org/math/li...eigenvectors-and-eigenspaces-for-a-3x3-matrix

It is very thorough.