Consider the example of solving a system of nonlinear equations by Newton's method, as given on Pages 95-97 of the Lecture notes. Write a program to carry out this iteration, using Gauss elimination to solve the 2 by 2 linear systems that arise. Use each of the following 16 initial data sets for the Newton iteration: (x^(0) _1, x^(0) _2 = (i, j), i = 0, 1, 2, 3, j = 0, 1, 2, 3. Present and discuss your numerical results in a concise manner. Consider the example of solving a system of nonlinear equations by Newton's method, as given on Pages 95-97 of the Lecture notes. Write a program to carry out this iteration, using Gauss elimination to solve the 2 by 2 linear systems that arise. Use each of the following 16 initial data sets for the Newton iteration: (x^(0) _1, x^(0) _2 = (i, j), i = 0, 1, 2, 3, j = 0, 1, 2, 3. Present and discuss your numerical results in a concise manner