% Hw4 Prob 6 and 7 MATLAB commands

% if you want all output to be printed as rational numbers, you can do so
% by the following command
format rational

fprintf(1,'Problem 6... \n\n');

A = [1 2 3 4 5
11 8 12 10 13
15 14 13 12 11
-2 -3 -4 -5 -6]

% saving a copy of A
A1=A; 

% replacement EROs to zero out lower entries in column 1 using the first
% entry
A(2,:) = A(2,:)-11*A(1,:);
A(3,:) = A(3,:)-15*A(1,:);
A(4,:) = A(4,:)+ 2*A(1,:)

% Swap R4 and R2, and then zero out other entries in column 2 using the
% second entry
A = A([1 4 3 2],:)
A(1,:) = A(1,:) -  2*A(2,:);
A(3,:) = A(3,:) + 16*A(2,:);
A(4,:) = A(4,:) + 14*A(2,:)

% Swap R3 and R4, and then scale the new R3 by (1/7)
A = A([1 2 4 3],:);
A(3,:) = A(3,:)*(1/7)

% zero out top two entries in column 3 using the pivot in 3rd row using
% replacement EROs
A(1,:)=A(1,:)+  A(3,:);
A(2,:)=A(2,:)-2*A(3,:)

% A total of 11 EROs were performed on A

% verify result using rref
Arref = rref(A1)

fprintf(1,'\nProblem 7... \n\n');

% Changing to the directory that has files from DL-LAA MATLAB toolbox
cd ../MATLAB/'MATLAB-Laydata Toolbox'/
c1s6
% Choose Exercise number 12; else, type in the augmented matrix
rref(A)