Prove that for the system \begin{cases} ax+by=p\\ cx+dy=q \end{cases} a necessary and sufficient condition of convergence for the Jacobi and Gauss-Seidel iterative methods is $|bc|<|ad|$.
I have tried to prove it using that the iterative method converges if and only if its espectral radius is $\rho<1$ without succeeding, however I am pretty sure I should use that