Consider the following system of nonlinear equations X1 X2 x3 = cos(x1) 81 sin (23) 3 + sin(x) cos(x3) 3 3 cos(x1) X2 sin (F3) + 9 3 6 + Perform three iterations by hand of successive substitution (using the obvious x = g(x) equations already given) starting from x = [1 1 1]. Compute the error relative to the exact solution x = [0 1/3 0]. Problem 2 (2 points) Perform by hand three iterations by hand of the Newton-Raphson method to solve the same system of Problem 1, again starting from x = [1 1 1]. Compute the error relative to the exact solution. Which method performs better? Explain your answer. Problem 3 (2 points) Solve the system of Problem 1 using a Python program: 1. Write a Python code to perform the successive iteration of Problem 1. Execute the iteration until the change in the norm of the solution relative to the previous iteration falls below = 1 x 10-4 (that is, until ||x(+)x(k)||/x(k)||