$\displaystyle \begin{bmatrix}-1&-1&1\\0&-2&1\\0&0&-1\end{bmatrix}$

Eigenvalues of the matrix are -1,-1,-2.

-1 with algebric multiplicity 2.

Eigenvectors for -1 are $\displaystyle \begin{bmatrix}1\\0\\0\end{bmatrix}$ and $\displaystyle \begin{bmatrix}0\\1\\1\end{bmatrix}$

I am finding difficulty in getting eigenvectors for -2.

$\displaystyle \begin{bmatrix}1&-1&1\\0&0&1\\0&0&1\end{bmatrix}\begin{bmatrix}x\\y\ \z\end{bmatrix}$=$\displaystyle \begin{bmatrix}0\\0\\0\end{bmatrix}$

How to solve this.

I am getting z=0,y=0,and x=y-z.

Can anyone help me.