Eigenvectors Question

Eigenvectors Question?
Characteristic polynomial:
x^3 - 3x - 2

Real eigenvalues:
{-1, -1, 2}

Eigenvector of eigenvalue -1:
(-1, 1, 0)
Eigenvector of eigenvalue -1:
(-1, 0, 1)
Eigenvector of eigenvalue 2:
(1, 1, 1)

I managed to get the eigenvector for eigenvalue 2 but for eigenvalue -1 I am getting stuck.

The matrix for the -1 value after matrix reduction is
1 1 1
0 0 0
0 0 0

Thank you for all the help


Additional Details
I managed to get the eigenvalues but it is the eigenvector for -1 that I can't get.

From the reduced matrix, x = -y - z
so the eigenvector is of (x, y, z) = (-y-z, y, z)

This is one eigenvector, which happens to be 2-dimensional.
(-y-z, y, z) = y(-1, 1, 0) + z(-1, 0, 1) = yi + zj

However, either i or j alone is not an eigenvector corresponding
to λ = -1.