hlsdk

%%Intro
%Setup constants and formatting
clear all
clc
digits(5);

MatrixRows = 5;
MatrixCols = 7;
VectorSize = 7;

%Setup random number generator
rand('state', sum(clock*100));

%Generate matrix A and vector u
A = vpa(rand(MatrixRows,MatrixCols));
u = vpa(rand(VectorSize,1));

%%Body
%Put matrix A into REF
A = rref(A)

%Calculate the product b = Au
b = A*u

%Solve for x by setting x = A\b
x = A\b

%Show augmented matrix produced by Ax = b or Au = b
U = rref([A b])

%%Conclusion
%Computing b as the product of A and u, we were able to solve for u by
%divinding A by b.

%Matlab shows b == x only when digits() or vpa() are on.

%There are infinitely many solutions because A has 2 free variables,
%corresponding to the last 2 columns.