%% Math 230 - Honors Introductory Linear Algebra 
%% MATLAB commands typed in Class on Tuesday, Feb 1, 2011

%% Lines that start with a '%' are comments - MATLAB ignores them
%% (i.e., does not "execute" or "run" them as commands).

% Exchange matrix for Prob 4, Page 63
A = [.65 .3 .3 .2
.1 .1 .15 .1
.25 .35 .15 .3
0 .25 .4 .4]

size(A)

A(1,2)
% gives the entry in the first row and second column
% In general, to access (i,j)-th element, we give A(i,j)

A(1,:)
% gives the first row, i.e., all elements in the first row

A(:,3)
% gives the 3rd column

A(1,1)-1
% subtract 1 from the (1,1) entry of A, and just print the result out
% without updating A(1,1)

A(1,1)=A(1,1)-1
% subtract 1 from the (1,1) entry of A, updating A(1,1) to the new value

A(1,1)=A(1,1)+1
% just going back to the original A(1,1) entry

Acopy = A;
% Creating a copy of A for future reference.
% semicolon at end suppresses printing of the output

% We need to do A(i,i) = A(i,i)-1 for i=1,2,3,4

1:4
% gives the numbers 1,2,3,4

% We use a "for" loop to do these repeated calculations
for i=1:4
 A(i,i) = A(i,i) - 1;
end

A

Arref = rref(A)
% reduced row echelon form of A


% But let's do some of the EROs ourselves
%
% Scale R1 by (1/-0.35) so that A(1,1) becomes 1

A(1,:)*(1/-0.35)
A(1,:) = A(1,:)*(1/-0.35)
% The second command above reassigns A(1,:).

% The replacement ERO R2-0.1xR1 (to zero out the entry in the (2,1)-position)
A(2,:) = A(2,:) - 0.1*A(1,:)

% swap R2 and R3
% we need to copy one of them to a temporary variable, and then effect the swap

r = A(2,:)
% second row is stored in r

A(2,:) = A(3,:);
A(3,:) = r

% Now R2 and R3 are swapped