% construct a linear system with solution [1;2;3]
A = rand(3,3)
b = A*[1;2;3]
%
B = [A,b]   % create an augmented matrix
Q = eye(3)  % initialize Q
%
G = givensmat(B(1:2,1))
B(1:2,:) = G*B(1:2,:)
Q(:,1:2) = Q(:,1:2)*G'
G = givensmat(B([1,3],1))
B([1,3],:) = G*B([1,3],:)
Q(:,[1,3]) = Q(:,[1,3])*G'
G = givensmat(B(2:3,2))
B(2:3,:) = G*B(2:3,:)
Q(:,2:3) = Q(:,2:3)*G'

x = backsub(B(:,1:3), B(:,4))