B = $\displaystyle \left(\begin{array}{ccc}4&0&-1\\0&4&1\\-1&1&3\end{array}\right)$

Find all the other eigenvalues and eigenvectors.

I have found the eigenvalues for this matrix being $\displaystyle \lambda = 2$, $\displaystyle \lambda = 4$ & $\displaystyle \lambda = 5$

I have subtracted your eigenvalues from the diagonal to get the following matricies

for $\displaystyle \lambda = 2$$\displaystyle \left(\begin{array}{ccc}2&0&-1\\0&2&1\\-1&-1&1\end{array}\right)$

for $\displaystyle \lambda = 5$$\displaystyle \left(\begin{array}{ccc}-1&0&-1\\0&-1&1\\-1&-1&-2\end{array}\right)$

My problem is that I am stuck on where to go from here. I have used the elimination method but I always end up with a row of zeros and am unsure on where to go from there.

Any help would be appreciated.