# Help with finding eigenvectors

Find eigen vectors for this:


I found that eigenvalues are $0,2,2$

And the eigen vector for $0$ is {$1,0,1$}

But I'm not sure how to find the eigenvector for $2$ since the matrix reduces to one equation. I already know what the eigenvectors are (from wolfram) however and there are two eigen vectors for $\lambda = 2$.

Any help would be great, Thanks

$$\ker{\left(\begin{bmatrix}1&1&-1\\0&2&0\\-1&1&1\end{bmatrix}-2I\right)}=\ker{\begin{bmatrix}-1&1&-1\\0&0&0\\-1&1&-1\end{bmatrix}}=\text{span}\left(\begin{bmatrix}1\\1\\0\end{bmatrix},\begin{bmatrix}1\\0\\-1\end{bmatrix}\right)$$