Guaranteeing convergence for Jacobi and Gauss-Seidel.

I'm given two 4x4 matrices F and G and told there are two systems of linear equations: Fx = f and Gy = g.

The questions asks if I can guarantee convergence for the matrices using Gauss-Seidel and Jacobi methods.

I find that F is strictly row diagonally dominant and say that convergence can be guaranteed.

Then find that G isn't row diagonally dominant and say convergence cannot be guaranteed.

The question then asks what the relevance of f and g are in the proof of convergence. Am I right in assuming they aren't relevant to the proof of convergence at all?

Thanks.