Construct a system of 4 nonlinear equations using the combination of sin (x), cos(xi), Xi2, x , exp(x), i = 1,2,3,4. The equation format looks like the following: f1 (x)= sin(x1) + 2X22-X3X42 + X4 = 0. You can use any combinations, but try to be relatively simple. Then, you will have the following system of 4 nonlinear equations: (x) = 0, f2(x) = 0, f(x) = 0, f(x)= 0 a) Write a matlab code to solve this problem using Newton's method. In each subroutine to solve this linear system using the LU decomposition with repeatedly call the subroutine of the linear systems to move forward. or in vector format: F(x) = 0. step, you need to solve a system of linear equations for the increment, write a pivoting plus forward and backward scheme. In the main program, you will b) Find all real roots by choosing proper starting values for x = 1,2,3,4. c) Use a predefined epsilon = 10-8 for the solution, i.e., making If(x) 10-8 In your loop, set Nmax-20 as the control to avoid getting into a dead-loop, i.e terminate the loop if n = 20. As we have learned in class, 4-6 iterations in Newton's method should be sufficient for most problems. To make the problem easier, you may start with a system of 2, then move on to system of 3 and finally solve for a system of 4 nonlinear equations. Construct a system of 4 nonlinear equations using the combination of sin (x), cos(xi), Xi2, x , exp(x), i = 1,2,3,4. The equation format looks like the following: f1 (x)= sin(x1) + 2X22-X3X42 + X4 = 0. You can use any combinations, but try to be relatively simple. Then, you will have the following system of 4 nonlinear equations: (x) = 0, f2(x) = 0, f(x) = 0, f(x)= 0 a) Write a matlab code to solve this problem using Newton's method. In each subroutine to solve this linear system using the LU decomposition with repeatedly call the subroutine of the linear systems to move forward. or in vector format: F(x) = 0. step, you need to solve a system of linear equations for the increment, write a pivoting plus forward and backward scheme. In the main program, you will b) Find all real roots by choosing proper starting values for x = 1,2,3,4. c) Use a predefined epsilon = 10-8 for the solution, i.e., making If(x) 10-8 In your loop, set Nmax-20 as the control to avoid getting into a dead-loop, i.e terminate the loop if n = 20. As we have learned in class, 4-6 iterations in Newton's method should be sufficient for most problems. To make the problem easier, you may start with a system of 2, then move on to system of 3 and finally solve for a system of 4 nonlinear equations