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_(1),x_(2),x_(3),x_(4)

, and

x_(5)

.\ Use MATLAB to construct the augmented matrix

Ab

and then perform row reduction using the rref() function. Write out your reduced\ matrix and identify the free and basic variables of the system.\ 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

.