# Find 2 linearly independent eigenvectors and a eigenvalue

1. Oct 8, 2008

### bodensee9

Hi

I am supposed to, without calculation, find 2 linearly independent eigenvectors and a eigenvalue of the following matrix A

5 5 5
5 5 5
5 5 5

The eigenvalue is easy -- it is 15. And I can find one eigenvector, [1 1 1] (written vertically), but another without calculation? Is there a trick that I should see? Of course, zero is also a eigenvalue, but how am I supposed to find the other eigenvector without calculation? Is there something that I should see?

Thanks.

2. Oct 8, 2008

### Dick

Re: eigenvalues/vectors

Pick the vector (x,y,z) so that 5x+5y+5z=0. Say, (1,1,-2)?

3. Oct 8, 2008

### bodensee9

Re: eigenvalues/vectors

oh thanks!