Question

Image transcription text

...

Competency

In this project, you will demonstrate your mastery of the following competency:

• Apply matrix theory to linear equations and transformations

Scenario

You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of 100+50 = 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers. These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as , , , , and .

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 equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to make your final answer as  where  is the  coefficient matrix,  is the  vector of unknowns, and  is a  vector of constants.
2. Use MATLAB to construct the augmented matrix  and then perform row reduction using the rref() function. Make out your reduced matrix and identify the free and basic variables of the system.
3.  Use MATLAB to compute the LU decomposition of , i.e., find . For this decomposition, find the transformed set of equations . Solve the system of equations  for the unknown vector .
4. Use MATLAB to compute the inverse of using the inv() function.
5. Compute the solution to the original system of equations by transforming  into , i.e., compute .
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 finish the 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.

Image transcription text

Southern New Hampshire University MAT 350 Project One Table Template Complete this template by replacing the bracketed text with the relevant information. + Network Recommended Solution Recommendation Explanation Link Capacity (Mbps) X1 60 [Insert text] [Insert text] [Insert text] X2 50 [Insert text] [Insert text] [Insert text] X3 100 [Insert text] [Insert text] [Insert text] XA 100 [Insert text] [Insert text] [Insert text] X5 50 [Insert text] [Insert text] [Insert text] O

...

Project One Template

MAT350: Applied Linear Algebra

Student Name

Date

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 do a 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:

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:

%code

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  using Cramer's Rule. Use MATLAB to compute the required determinants using the det() function.

Solution:

%code

Problem 7

The Project One Table Template, provided in the Project One Supporting Materials section in Brightspace, 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.

Solution:

Fill out the table in the original project document and export your table as an image. Then, use the Insert tab in the MATLAB editor to insert your table as an image.

This template is the starting point for your solution to this project. Download the template, open in MATLAB, and complete each portion. Solved by verified expert

sum dolor sit amet, consectetur adipiscing eli

dictum vitae odio. Donec aliquet.

or nec facilisis.

lestie consequat, ultrices ac magna. Fusce dui lectus, congu

a. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacin

Explore over 16 million step-by-step answers from our library

Step-by-step explanation

iscing elit. Nam lacini

ce dui lectu

facilisis. Pellentesque dapibus efficitur laoreet.

cing elit. Nam lacinia pulvinar tortor nec facilis

ac, dictum vitae odio. Donec aliquet. Lorem ipsum d

ng elit. Nam lacinia pulvinar tortor nec facilis

congue vel laoreet ac, dictum vitae odio. Don

entesque dapibus efficitur

m ipsum dolor sit amet, consecte

a. Fusce dui lectus, congue vel

, dictum vitae odio. Donec aliqu

icitur laoreet. Nam risus ante,

gue

s a molestie

e vel laoreet ac, d

risus ante, dapibu

entesque dapibu

Fusce dui lectus,

congue vel

ctum vitae od

o. Donec aliquet. Lorem ipsum dolor

ac, dictum vitae odi

Donec aliquet. Lorem ipsum dolor sit amet, consec

trices ac magna. Fusce dui lectu

gue

trices ac magna. Fusce dui lectus,

sum dolor sit am

usce dui lectus, congue vel

ongue vel laoree

ce dui lectus, congue vel

Fusce dui lectus

ec aliquet. Lorem ipsum

ctum vitae odio.

gue

ec facilisis. Pel

ec aliquet. Lorem ipsum dolor sit amet, con

fficitur laoreet. Nam

s ante, dapibus a molestie

gue

molestie consequat, ultrices

gue

ac, dictum vitae odio. Donec al

s ante, dapibus a molestie

gue

dictum vitae odio. Donec aliq

icitur laoreet. Nam risus a

gue