# MAT 350 AMC System of Linear Equations & Reduced Matrix MATLAB Project

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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 U using the inv() function.
5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = U^-1y.