Hey guys, just got into computing eigenvectors and values just last week, and found that this thing in my homework, typically the ones on the homework were easy, but this one threw me off, and im not sure why.

Find the Eigenvalues and Eigenvectors of $\displaystyle C= \left(\begin{array}{ccc}1&1&0\\0&1&0\\0&0&1\end{ar ray}\right) $ if you can, diagonalize C as well.

So my work is basically this, I computed the eigenvalue of c=1 with algebraic multiplicity = 3, stuck it into B-cI, where c is the eigenvalue coresponding to B, and I is the identity matrix, and got a reduced matrix with with wierd results...i mean can an eigenvector be the zero vector? If anyone could show me how they got their eigenvectors as a result would be greatly helpful.