Associate two linearly independent eigenvectors

Question

Problem:

Eigenvalues and Eigenvectors

The matrix A = 1 1 0
                        0 0 0
                        0 1 1

has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2.

Find the eigenvalues and the eigenvectors.

Eigenvalue of multiplicity 1 :

Associated Eigenvector:

Eigenvalue of multiplicity 2 :

Associated two linearly independent eigenvectors:

If you have a floating point number ending in e-16 or some such thing, treat this as zero. All entries in your matrix should be integers.