Question

# I need help to identify how to write a system of linear equations...

I need help to identify how to write a system of linear equations for the A,B,C,D,E Router locations and x1,x2,x3x,x4,x5 data rate nodes. The system will be calculated in MATLAB, differences from x1 =60, x2=50, x3=100, x4=100, x5=50 will need to be submitted as recommendations to the system.

Scenario

The communication network shows the sender transmitting 100 Mbps of data to router A and 50 Mbps of data to router C. From router A, there is an arrow labeled X₁ pointing to router C and an arrow labeled X₁ pointing to router B, and an arrow labeled X₂ pointing to router E. From router B, there is an arrow labeled X₅ pointing to router E and an arrow labeled X₃ pointing to the receiver. From router C, there is an arrow labeled X₃ pointing to router E and an arrow labeled X₅ pointing to router D. From router E, there is an arrow labeled X₄ pointing to router D. From router D, there is an arrow labeled X₂ pointing to router B and an arrow showing 120 Mbps of data being transmitted to the receiver.

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 x one, x two, x three, x four, and x five.

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.

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 submit final answer as Matrix A times vector x equals vector b where The matrix A is the five-by-five coefficient matrix, The vector x is the five-by-one vector of unknowns, and The vector b is a five-by-one vector of constants.

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