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.

Write a program that reads in a series of lines of input character by character (using the library function the first line of the input contains an integer which specifies the number of remaining lines of input, each of which contains a floating point number. the integer value on the first line can be read with (the library function) but all of the following lines can only be read with each line, after the first, contains a single floating point value, with up to four digits before the decimal point, and up to four digits following the decimal point, but there is not necessarily a decimal point in each number; i.e., it may appear to be an integer, but the digits should be read by your program, and the number should be converted to a corresponding floating point number. for instance, suppose the following input: 5 3.1255 20.25 0.875 1921.50 31 the required output is: − each of the input floating point values, printed on a separate line with four digits of precision, using printf(); − on the last line of the output, the string “total: ” followed by the sum of the input values, printed with printf() to 4 digits of precision. for example, the total of the sample input given above is 1976.7505, so the required output for this input would be: 3.1255 20.2500 0.8750 1921.5000 31.0000 total: 1976.7505 do not concern yourself with small differences in the total due to rounding, as the grader will not deduct points for this. constraints: − you are not allowed to use arrays on this portion of the lab assignment. − there is no maximum number of lines allowable. it all depends upon the first value of input. since you aren’t saving anything, it doesn’t matter. − you can assume that input will not contain more than 4 digits before or after the decimal point. you do not need to error check for this condition. -you must use getchar() to read in the floating point values one character at a time (i.e. do not use -you must declare and use your floating point values as a double to minimize rounding errors. -only use printf() to output the floating point numbers and the total (do not use − be sure your directions to the user are clear so they are sure to enter the input data correctly.