
 a) Verify with numeric applications, 
    the properties of the determinant. 
    
 b) The coefficients, integers or fractions, are randomly
    selected by the computer.

 c) The size of the matrices, are randomly selected by the 
    computer, but you can select the size if you want.

 
    Try the examples in this order.

       dc0f.c     dc0i.c  :  If A has a column of zeros det(A) = 0
       dr0f.c     dr0i.c  :  If A has a row    of zeros det(A) = 0

    dtrposf.c  dtrposi.c  :  det(A) = det(TrposA)

                             If A has a zero on its diagonal det(A) = 0,
    ddiag0f.c  ddiag0i.c  :  Diagonal matrices.
   dltri0ff.c dltri0fi.c  :  Lower Triangular matrices.
   dutri0ff.c dutri0fi.c  :  Upper Triangular matrices.
                      
                             The determinant of,
     ddiagf.c   ddiagi.c  :  a diagonal matrix,
     dltrif.c   dltrii.c  :  a lower    matrix,
     dutrif.c   dutrii.c  :  a upper    matrix.

                             If B is the matrix that results when,
     dkcolf.c   dkcoli.c  :  a single column of A is multiplied by k, then det(B) = k det(A),
     dkrowf.c   dkrowi.c  :  a single row    of A is multiplied by k, then det(B) = k det(A).

                            If B is the matrix that results when,
    drow12f.c  drow12i.c  : two rows    are interchanged then det(B) = - det(A)
    dcol12f.c  dcol12i.c  : two columns are interchanged then det(B) = - det(A)

     detabf.c   detabi.c  : det(A) det(B) =   det(AB)

      dinvf.c    dinvf.c  :     det(invA) = 1/det(A)






       