I have the matrix \begin{bmatrix}1&0&0\\2&2&-1\\0&1&0\end{bmatrix} I know that the only eigenvalue is 1 with multiplicity 3
I solved for the first eigenvalue and got \begin{bmatrix}0\\1\\1\end{bmatrix}
How do I find the other two? I know they are \begin{bmatrix}0\\1\\0\end{bmatrix} and \begin{bmatrix}1/2\\0\\0\end{bmatrix} but when I do $(A-\lambda I)v_2 = v_1$, I get the system of equations $2x + y -z = 1$, $y -z =1$. I don't see how that gives the second eigenvector.
Thanks