disp('A semi-automatic example for Gauss-Jordan elimination')
pause
disp('First create a random matrix')
A=rand(4,5)
pause
disp('Then make this into an integer matrix with reasonable numbers')
A=100*A
A1=floor(A)
pause
disp('Unless the random number generator created some zeros we need')
disp('not make row interchanges -- else simply start over again, or')
disp('use a more sophisticated program that checks for zero entries.')
%
pause
disp('Forward elimination: The first column.')
A2=r1(A1,1,1/A1(1,1))
pause
A3=r3(A2,1,-A2(2,1),2)
pause
A4=r3(A3,1,-A3(3,1),3)
pause
A5=r3(A4,1,-A4(4,1),4)
pause
disp('Forward elimination: The second column.')
A6=r1(A5,2,1/A5(2,2))
pause
A7=r3(A6,2,-A6(3,2),3)
pause
A8=r3(A7,2,-A7(4,2),4)
pause
disp('Forward elimination: The third column.')
A9=r1(A8,3,1/A8(3,3))
pause
A10=r3(A9,3,-A9(4,3),4)
pause
disp('Forward elimination: The fourth column.')
A11=r1(A10,4,1/A10(4,4))
pause
disp('Backward elimination: The fourth column.')
A12=r3(A11,4,-A11(1,4),1)
pause
A13=r3(A12,4,-A12(2,4),2)
pause
A14=r3(A13,4,-A13(3,4),3)
pause
disp('Backward elimination: The third column.')
A15=r3(A14,3,-A14(1,3),1)
pause
A16=r3(A15,3,-A15(2,3),2)
pause
disp('Backward elimination: The second column.')
A17=r3(A16,2,-A16(1,2),1)
pause
disp('And a little faster using rrefmovy')
A1=A;
rrefmovy(A1)
pause
disp('Next using the MATLAB built-in rrefmovie')
pause
A1=A;
rrefmovie(A1)
pause
disp('And finally, we no longer care about the intermediate steps:')
A1=A;
rref(A)