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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!

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    I need the solutions for this system of equations as I can't work it out for some reason.2012-12-02
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    Yeah, I guess you meant(1,-2,1) in the first part of the WA command? Yeah, I get it when y = 0, z = -x and that's a solution? And if z=0, x=2y and if x=0, z = 2y?2012-12-02

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