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Snhu mat 350 project one

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Project One MAT350: Applied Linear Algebra Gary Bixby November 15, 2020 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 write your 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: Since, input = output: A has 100Mbps coming in, x1 output going to B and C, an x2 output going to E. Therefore, A can be catpured as: 2x1 + x2 = 100 B has x1 and x2 as inputs, x3 and x5 as outputs. Therefore: x1 + x2 = x3 +x5 OR x1 + x2 - x3 - x5 = 0 C has 50 Mbps and x1 as input, x3 and x5 as outputs. Therefore: 50 + x1 = x3 + x5 OR x1 - x3 - x5 = -50 D has an output of 120Mbps and x2, inputs of x4 and x5. Therefore 120 + x2 = x4 + x5 OR x2 - x4 - x5 = -120 E has inputs of x2, x3, and x5; output of x4. Therefore x2 + x3 + x5 = x4 OR x2 + x3 - x4 + x5 = 0 1 The Ax = b matrix then, is as follows: = 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: RowReducedAb = 1 0 0 0 0 25 0 1 0 0 0 50 0 0 1 0 0 30 0 0 0 1 0 125 0 0 0 0 1 45 There are no free variables. %code %Coefficient matrix A A = [2 1 0 0 0; 1 1 -1 0 -1; 1 0 -1 0 -1; 0 1 0 -1 -1; 0 1 1 -1 1] A = 5×5 2 1 1 0 0 1 1 0 1 1 0 -1 -1 0 1 0 0 0 -1 -1 0 -1 -1 -1 1 %Column ...
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