% A-2 Q-1(a)
A = [5 -1 1
    2 8 -1
    -1 2 4];
b = [10
    11
    3];

D = diag(diag(A));
LU = D - A;

f = @(x) (D\LU)*x + D\b;

x0 = [0;0;0];
x = f(x0);
while norm(x-x0) > 0.0001
    x0 = x;
    x = f(x);
end

disp(x)


% A-2 Q-1(b)
A = [5 -1 1
    2 8 -1
    -1 2 4];
b = [10
    11
    3];

D = diag(diag(A));
L = D - tril(A);
U = D - triu(A);

f = @(x) ((D-L)\U)*x + (D-L)\b;

x0 = [0;0;0];
x = f(x0);
while norm(x-x0) > 0.0001
    x0 = x;
    x = f(x);
end

disp(x)


% A-2 Q-1(c)
A = [5 -1 1
    2 8 -1
    -1 2 4];
b = [10
    11
    3];

D = diag(diag(A));
L = D - tril(A);
U = D - triu(A);

f = @(x) ((D-L)\U)*x + (D-L)\b;

x0 = [0;0;0];
x = f(x0);
w = 0.5;
while norm(x-x0) > 0.0001
    t = x0;
    x0 = x;
    x = (1-w)*t + w*f(x);
end

disp(x)