clc;
clear all;
close all;

format long e;
E = 0.01;
A = [1,2; 1, 2+E];
b = [4;4+E];

x1c = det([4, 2; 4+E, 2+E]) / det(A);
x2c = det([1,4; 1,4+E]) / det(A);

% disp(x1c);
% disp(x2c);

Ainv = inv(A);
xinv = Ainv * b;
Z = [A b];
Z(1,:) = Z(1,:) / Z(1,1);
Z(2,:) = Z(2,:) - Z(1,:)*Z(2,1);

% disp(Z);
x2g = Z(2,3) / Z(2,2);
% disp(x2g);
x1g = (Z(1,3) - 2 * x2g) / Z(1,1);
% disp(x1g);

[q,r] = qr(A);
xqr = inv(r) * q' * b;
% disp(xqr);

Yqr = q' *b;
Xqr = inv(r) * Yqr;
% disp(Xqr);

[U,S,V] = svd(A);
Xsvd = inv(V) * inv(S) * U' * b;
% disp(Xvd);

[L,U] = lu(A);
Xlu = inv(U) * inv(L) * b;
% disp(Xlu);
y = inv(L) * b;
Xlu2 = inv(U) * y;
disp(Xlu2);