Consider the network with adjacency matrix A given by

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. 2. 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, where y = Ux. Solve the system of equations Ly = b for the unknown vector y. 4. Compute the inverse of U using the inv() function. 5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y 6. Check your answer for x1 using Cramer’s Rule. Use MATLAB to compute the required determinants using the det() function.

A fixed beam is subjected to a uniformly-distributed load with an intensity of f = 10 N/mm length of L = 200 mm. Now determine the support reaction forces, internal shear forces and moments, then plot its internal shear force and moment diagram. f[N/m] L 1. Define the paramters, use L and f as the variables y X

How do I find the minimum capacity of an s-t cut in this flow network?