Finding the eigenvalues of a 4x4 matrix So I have this matrix $A$, so after I did $\det(xI-A)$, I have this 
\begin{pmatrix}
        x & 0 & 0 & -x \\
        0 & x & 0 & -2x \\
        0 & 0 & x & -2x \\
          -1 & -1 & -1 & x-1 
        \end{pmatrix}
At this point I'm contemplating taking out an $x$ out of the matrix but there is a $-1$ on the bottom row.  How can I go about row reducing this matrix?

$A  = \pmatrix {1&1&1&1\\2&2&2&2\\2&2&2&2\\1&1&1&1}$
Since A is a singular matrix, we know that 0 is an eigenvalue.
So, what is the dimension of the kernel of A?
if we perform row operations on A we get
$A  = \pmatrix {1&1&1&1\\0&0&0&0\\0&0&0&0\\0&0&0&0}$
The dimension of the kernel is 3
0 is an eigenvalue of multiplicty 3
The sum of the eigenvalues equals the trace of the matrix.
The trace of A is 6
The remaining eigenvalue is 6
