Problem 4. Write a Matlab code for Newtons method to find a (nonzero) root of the system x x2y2 =0, yx2+y2 =0 starting with x0 = 0.5,y0 = 0.5. Use format long and stop when both components of two successive iterates agree to 14 decimal places. Display the approximations given and the size of the functions at each iteration. To solve the ensuing linear system, e.g. Ax = b, use the command x = A \ b;

Problem 5. Solve the same problem as Problem 4 using Matlabs fsolve routine. To run this program, type options = optimset(Display, iter); x0 = [0.5,0.5] [x,fval] = fsolve(@fcnns,x0,options) where fcnns is the name of the M-file defining the functions. Note that Matlab expects the functions to be defined as a vector.