proof of matrix singularity If anyone can help me with the next question I would appreciate it a lot.
Let $A$ and $B$ be $n*n$ matrices and let $C=A-B$. Show that if $Ax_0=Bx_0$ and  $x_0$ is not zero, then $C$ must be singular.
The first thing I don't get is the notation, what do $Ax_0$ and $Bx_0$ mean?
Thanks in advance :)

Presumably, $x_0$ is any non zero vector of the space where the matrices apply, and $Ax_0$, $Bx_0$ are the products of these matrices and this vector.
