% Sample script for typical in-class first-try to implement
% Graham Schmidt Orthogonalization in one special example.
% The start vectors are typical for students choices.....
%
% All rights reserved.    Original version: Nov 2003
% Matthias Kawski         http://math.asu.edu/~kawski

v1=[1 2 3]'
v2=[3 4 5]'
v3=[5 7 10]'
check_rank=rref([v1 v2 v3])
u1=v1/sqrt(v1'*v1)
w2=v2-(u1'*v2)*u1
u2=w2/sqrt(w2'*w2)
w3=v3-(u1'*v3)*u1-(u2'*v3)*u2
u3=w3/sqrt(w3'*w3)
U=[u1 u2 u3]
check=U'*U