%% Homework template for the Matlab part of 6.3:
% Here is an 8 x 4 matrix U (Exercise 35, Section 6.2)
U=[-6 -3 6 1
    -1 2 1 -6
    3 6 3 -2
    6 -3 6 -1
    2 -1 2 3
    -3 6 3 2
    -2 -1 2 -3
     1 2 1 6];


%% Our formulas are only valid for columns with o.n. columns:
%  (in class) Compute U^T U
U'*U
%  (in class) What does this tell you about the columns of U?
%  Answer:  The columns are orthogonal- They would be o.n. if we divide by
%           10.  There may be numerical round off error:
U=U/10;
U'*U

%% (#25, 6.3)  Find the distance between y given below and Col(U)
y=ones(8,1);


%% (#26, 6.3)  Addition:  Find the projection of b onto Col(U), then find
%              the distance between b and col(U)

b=[ones(4,1); -ones(4,1)];