I agree with your first eigenvalue=2 and eigenvector=(1,0,1).
Can you see the other 2 sets,
eigenvalue =2, eigenvector = (0,1,0)
eigenvalue =-8, eigenvector = (1,0,-1)?
I have found the eigenvalues for the above matrix to be, , it occurs twice.
When i plug my eigenvalue of 2 back into the matrix to find the eigenvectors i get;
So i said my chose my first eigenvector, v1 to be;
Trouble is i need another 2 vectors V2 and V3 such that:
v1.v2 = 0
v1.v3 = 0
v2.v3 = 0
where v1, v2, v3 are all unit vectors.
Im hoping to find the matrix O where v1,v2,v3 are O's columns
I posted this question earlier but i think its phrasing was a bit messy so i tried using LaTex for the first time...