Directions In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system can be modeled mathematically as a system of...

Directions

In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these equations can be written by noting that the sum of inputs must equal the sum of outputs.

To complete the project, work on the problems described below. As you complete each part, show your work and carefully describe how you arrive at your final answer. The methods and conclusions need to be clear when sharing your results with management. Any MATLAB code or MATLAB terminal outputs you generate should be provided in your submitted document to support your answers and work.

1. 
   Develop a system of linear equationsfor the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer aswhereis thecoefficient matrix,is thevector of unknowns, andis avector of constants.


2. Use MATLAB to construct the augmented matrixand then perform row reduction using the rref() function. Write out yourreduced matrix and identify the free and basic variables of the system.


3. Use MATLAB tocompute the LU decomposition of
   , i.e., find. For this decomposition, find the transformed set of equations. Solve the system of equationsfor the unknown vector.


4. Use MATLAB tocompute the inverseofusing the inv() function.


5. 
   Compute the solution to the original system of equationsby transforminginto, i.e., compute.


6. 
   Check your answer forusing 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 recommendationsfor 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,explainhow 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.

Supporting Materials