# MATLAB problem (#8) from Homework 5

A = 10*rand(4,6)
B = A(:,[2 5 1 4 6 3])
C = rref(A)
D = rref(B)

fprintf(1,'\n C and D are not the same matrix.\n\n');

E = C(:,[2 5 1 4 6 3])

fprintf(1,'\n E and D are not the same matrix either.\n But reduced echelon of E should be the same as D.\n\n');

Erref = rref(E)


%%%%%%%%%%%%%%% OUTPUT FROM MATLAB %%%%%%%%%%%%%%%%%%%%%%%

A =
    8.1472    6.3236    9.5751    9.5717    4.2176    6.5574
    9.0579    0.9754    9.6489    4.8538    9.1574    0.3571
    1.2699    2.7850    1.5761    8.0028    7.9221    8.4913
    9.1338    5.4688    9.7059    1.4189    9.5949    9.3399
B =
    6.3236    4.2176    8.1472    9.5717    6.5574    9.5751
    0.9754    9.1574    9.0579    4.8538    0.3571    9.6489
    2.7850    7.9221    1.2699    8.0028    8.4913    1.5761
    5.4688    9.5949    9.1338    1.4189    9.3399    9.7059
C =
    1.0000         0         0         0   17.2819   11.5872
         0    1.0000         0         0    0.8395    2.4249
         0         0    1.0000         0  -15.9067  -11.3994
         0         0         0    1.0000    1.0883    0.6236
D =
    1.0000         0         0         0    1.8233    0.0528
         0    1.0000         0         0    0.7166   -0.0629
         0         0    1.0000         0   -0.7977    1.0865
         0         0         0    1.0000   -0.1563    0.0684

 C and D are not the same matrix.

E =
         0   17.2819    1.0000         0   11.5872         0
    1.0000    0.8395         0         0    2.4249         0
         0  -15.9067         0         0  -11.3994    1.0000
         0    1.0883         0    1.0000    0.6236         0

 E and D are not the same matrix either.
 But reduced echelon of E should be the same as D.

Erref =
    1.0000         0         0         0    1.8233    0.0528
         0    1.0000         0         0    0.7166   -0.0629
         0         0    1.0000         0   -0.7977    1.0865
         0         0         0    1.0000   -0.1563    0.0684