4. From Divergence to Convergence for Iterative Methods Although some systems will have coefficient matrices that lead to divergence in iteration methods, they can be converted to equivalent systems for which the method will converge. The following exercise illustrates this idea on a simple example. Consider the system with Ax = b 5 1 0 A = 10 -1 1 -15 -4 4 b= H (a) Show that Gauss-Jacobi will diverge. Note that testing diagonal dominance does not suffice for showing divergence. (b) Using elementary row operations, convert the system to the equivalent system Ax = b with A having zeros in the first column below the 1, 1 entry. Show that A is diagonally dominant, hence proving that Gauss-Jacobi will converge.