hlsdk

%%Intro
%Setup constants
clear all
clc
MatrixRows = 15;
MatrixCols = 15;

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

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

%%Body
%Solve Ax = b by x = A\b
x = A\b

%Solve Ax = b by U = rref([A b])
U = rref([A b]);
y = U(:,MatrixCols+1)

R = b - A * x
S = b - A * y

%%Conclusion
%Matlab reports that both x = y, and that R = S, within floating point
%precision