I'll start you off.

Find your charpoly:

The roots of this quadratic are your eigenvalues.

They are 1 and 6.

Sub them in for lambda in the matrix we derived, getting:

Use rref on these matrices and we find:

Your solutions are:

, respectively.

Bases for the eigenspace are:

Let this be P:

Now, find . You have all the necessary info.

Check me out. Easy to flub up.

I hope this helps.

If you don't have one, get a good linear algebra text. Anton and Rorres publish some good ones.