4. (a) Can Jacobi and Gauss-Seidel converge for non-diagonally dominant systems? Explain.
(b) Consider the following linear system,
x + z = 2,
-x + y = 0,
x + 2y - 3z = 0.
Is the coefficient matrix associated to this linear system diagonally dominant? Apply Jacobi and Gauss-Seidel to this system with different initial guesses. Do the iterations converge? For which initial guesses do the iterations converge? [Hint: start with the exact solution, and modify each of its elements in turn to get different initial guesses.]