Eigenvectors and Kernel of Matrix I'm trying to take find the eigenvectors of the matrix
$$
\begin{bmatrix}
1 & 1 & 0 \\
0 & 1 & 0 \\
0 & 0 & 0
\end{bmatrix}.
$$
I've found the eigenvalues of $1$ and $0$. I'm very confused how to find the kernel of $E0$ and $E1$. How do I go about doing this?

Both $A$ and $A-I$ are in row echelon form and so solving the kernel for your $E_0$ and $E_1$ can be done automatically by looking at the two matrices without any row reductions.
