I'm trying to answer this question, but am completely stuck.

Argue that in analyzing the error in a stationery linear relaxation scheme applied to $\displaystyle Au=f$, it is sufficient to consider $\displaystyle Au=0$ with arbitrary initial guess, (say $\displaystyle v_0$).

Any ideas?

I'm not even sure what the author is trying to say, is he saying when studying the error produced by the relaxation method (eg. the jacobi method) it is sufficient to study the error of the associated homogenous system $\displaystyle Au=0$ with arbitrary initial guesses (say $\displaystyle v_0$). But in this case the error will simply be $\displaystyle e=-v_0$. (since the error is defined as $\displaystyle e=u-v_0$)

Maybe the residual equation plays a part, $\displaystyle Ae=r$ ... ???

Any help, would be much appreciated