OK so on my homework it says Diagonalize the following matrix, if possible:

[3 2 -2]

[0 2 0]

[0 1 3]

I found out the eigenvalues which is 2 and 3. 3 is a repetition so that's why there's only 2.

Now I'm suppose to find the eigenvalue. But I have no clue how to find the eigenvector. I'm readingm y textbook and the only thing that happens is they give me the eigenvalue then mysteriously find the eigenvector within one step.