Let A,b be the same 100100 matrix and 100 -dimensional vector Aij=2.0110ifi=jifi=j1,otherwisebi=1001sin(502i) A=(10.9991.0011) Ax=b,b=(11),Ax~=b~,b~=(11.001) Ax=b descent method 1. Start with a vector x0 with randomly chosen elements in the range 1(x0)i1 (i.e. with elements generated from what the function numpy .random.rand() or a similar replacement returns). 2. Run 200 iterations and plot the values of (x(k))i against i for every few iterations, for example k=0,2,5,10,20,50,100,200. Work on the following tasks: a) Write a program for the Gauss-Seidel method to solving Ax=b. b) Write a program for the steepest descent method to solving Ax=b. c) Compare the results between the Gauss-Seidel and the steepest descent method. How do they perform compared to the Jacobi method Let A,b be the same 100100 matrix and 100 -dimensional vector Aij=2.0110ifi=jifi=j1,otherwisebi=1001sin(502i) A=(10.9991.0011) Ax=b,b=(11),Ax~=b~,b~=(11.001) Ax=b descent method 1. Start with a vector x0 with randomly chosen elements in the range 1(x0)i1 (i.e. with elements generated from what the function numpy .random.rand() or a similar replacement returns). 2. Run 200 iterations and plot the values of (x(k))i against i for every few iterations, for example k=0,2,5,10,20,50,100,200. Work on the following tasks: a) Write a program for the Gauss-Seidel method to solving Ax=b. b) Write a program for the steepest descent method to solving Ax=b. c) Compare the results between the Gauss-Seidel and the steepest descent method. How do they perform compared to the Jacobi method