So I have \begin{align*} x - 2y + z & = 0 \\ -2x + 4y - 2z & = 0 \\ x - 2y + z & = 0 \end{align*}
I know I need to find two eigenvectors for the eigenspace with eigenvalue 2 as I know the matrix is diagonalizable and I've already found the eigenvector for the eigenspace with eigenvalue 8...
I can't seem to solve this. Please help!