# Math Help - Eigenspaces

1. ## Eigenspaces

I needed to find the eigenvalues for the matrix
5 0 1
1 1 0
-7 1 0

Which I found to be 2 with multiplicity 3.

Now I am required to find the eigenspace, and therein describe it geometrically.

I believe that I am supposed to use this:

det(2I-A)=0

and then subsequently row reduce the augmented matrix to find the solution.
I end up with an identity matrix with a column of zeroes, which would then mean that the matrix has only the trivial solution. Have I done this incorrectly? And if not, how do I describe this geometrically?

2. You would like to find all $\vec v$ such that

$A \vec v=2\vec v$

or equivalently

$(2I-A)\vec v=0$.

Now you should see that you need to find

$null(2I-A)$