PLEASE HELP WITH PROBLEM 6!!

Problem 1 Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax=b where A is the 5x5 coefficient matrix, x is the 5x1 vector of unknowns, and b is a 5x1 vector of constants. Solution: %code A = [2 1 0 0 0; 1 1 -1 0 -1; 1 0 -1 0 -1; 0 -1 0 1 1; 01 1 -1 1]; b = [100; 0; -50; 120; 0] b = 5x1 100 50 126Problem 2 Use MATLAB to construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced matrix and identify the free and basic variables of the system. Solution: %%code Ab = [A b] Ab = 5x6 OOHIN HOPP HOHKO H HOO O HHHHO 100 O rreduc = rref(Ab) rreduc = 5x6 OOOHO OOHOO OHOOO HOOOO 12Problem 3 Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations Ly = b, where y = Ux. Solve the system of equations Ly = b for the unknown vector y. Solution: %code [L U] = lu(A) L = 5x5 1. 0000 0. 5000 0. 5000 1. 0000 1. 0000 0. 5000 0. 5000 1. 0000 e 1. 0000 e -1. 0000 -1. 0000 0. 5000 1. 0000 U = 5x5 2. 0000 1. 0000 -1. 0000 1. 0000 1. 0000 OO -1 . 0000 0. 5000 -1. 5000 1. 0000 1. 0000 1. 0000Problem 4 Use MATLAB to compute the inverse of U using the inv() function. Solution: %code y = linsolve(L, b) y = 5x1 100 120 -160 170 45Problem 5 Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y. SoNon: %code x = iax(U)*y x = 5X1 25 56 36 125 45 Problem 6 Check your answer for x, using Cramer's Rule. Use MATLAB to compute the required determinants using the det() function. Solution: %code