In Exercises 1 and 2, compute the first four iterates, using the zero vector as the initial approximation, to show that the Gauss-Seidel method diverges. Then show that the equations can be rearranged to give a strictly diagonally dominant coefficient matrix, and apply the Gauss-Seidel method to obtain an approximate solution that is accurate to within 0.001.
1. x1 - 2x2 = 3
3x1 + 2x2 = 1
2. x1 - 4x2 + 2x3 = 2
2x2 + 4x3 = 1
6x1 - x2 - 2x3 = 1