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 5 x 5 coefficient matrix, x is the 5 x 1 vector of unknowns, and b is a 5 x 1 vector of constants. 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.
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. Solve the system of equations Ly = b for the unknown vector y.
4. Use MATLAB to compute the inverse of Uusing the inv() function.
5. Compute the solution to the original system of equations by transforming y into x, i. e., compute x = U-ly.
6. Check your answer for Xi using Cramer's Rule.
7. Use MATLAB to compute the required determinants using the det() function. The Project One Table Template, provided in the Supporting Materials section, shows the recommended throughput capacity of each link in the network. Put your solution for the system of equations in the third column so it can be easily compared to the maximum capacity in the second column. In the fourth column of the table, provide recommendations for how the network should be modified based on your network throughput analysis findings. The modification options can be No Change, Remove Link, or Upgrade Link. In the final column, explain how you arrived at your recommendation. What to Submit To complete this project, you must submit the following: Use the provided Project One Template as the starting point for your project solution. Complete each portion of the template, run the project, and then export your work as a single PDF file. Upload this PDF document, which should show your answers and supporting work for the problems described above. Make sure to include explanations of your work, as well as all MATLAB code and outputs of the computations.