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?