1. ## Finding eigenvectors

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?

2. Originally Posted by nukenuts
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....
You don't? How about z = 0, 2x + y = 0, for x not equal to 0?

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?
Here z = 0, and therefore x = 0, but y is allowed to be anything except zero. This is all assuming you've done your row reduction correctly. I haven't checked that.

3. How did I miss that? Thanks for pointing it out mate.

4. You're welcome!