Problem 5 Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y. Solution: %code Problem 6 Check your answer for x using Cramer's Rule. Use MATLAB to compute the required determinants using the det() function. Solution: %code 1 3 4 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: Put your math/explanation here... Problem 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 Problem 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 Problem 4 Use MATLAB to compute the inverse of U using the inv() function. Solution: