In Exercises 1 and 2, the coefficient matrix is not strictly diagonally dominant, nor can the equations be rearranged to make it so. However, both the Jacobi and the Gauss-Seidel method converge anyway. Demonstrate that this is true of the Gauss-Seidel method, starting with the zero vector as the initial approximation and obtaining a solution that is accurate to within 0.01.
1. - 4x1 + 5x2 = 14
x1 - 3x2 = - 7
2. 5x1 - 2x2 + 3x3 = - 8
x1 + 4x2 - 4x3 = 102
- 2x1 - 2x2 + 4x3 = - 90