Just out of my exam there and I it went fine except for one question. Getting the eigenvalues and eigenvectors of

1 0 8

4 3 12

0 0 7

I got eigenvalues of 1,3 and 7. However when I used the equation (A-λI)v = 0 for these values I couldnt get a correct answer. For example when λ = 1 I get

(0 0 8 ) x = 0

(4 2 12) y = 0

(0 0 6 ) z = 0

That gives -

8z = 0

4x + 2y + 12z = 0

6z = 0

So I get no solution....

When I take λ = 3 I get

(-2 0 8 ) x = 0

(4 0 12) y = 0

(0 0 4 ) z = 0

and that gives

-2x + 8z = 0

4x + 12z = 0

4z = 0

...

So how am I supposed to find the eigenvectors?