close all; clc; clear; 

% Problem EPage 46
% 
A = [ 2, -3, 2 ; 1.9, -3, 2.2 ; 2.1 -2.9 2 ; 6.1 2.1 -3 ; -3 5 2.1 ];
b = [ 1.01 ; 1.01 ; 0.98 ; 4.94 ; 4.10 ];
x_backslash = A \ b;

x_pinv = pinv(A) * b;

% A x = b => 
% Q R x = b
%
[Q,R] = qr(A);

% Then R x = Q' b 
%
q_times_b = Q' * b;

% Solve this tridiagonal system: 
%
x_qr = R \ q_times_b ;

% Show that all solutions are the same: 
% 
[ x_backslash.' ; x_pinv.' ; x_qr.' ]