
 a) Verify with numeric applications, 
    some basic properties and theorems V. 
    
 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.

                           Let A be a fixed m x n matrix.
                        Find all m x 1 matrices b such that
                   the system of equation Ax = b is consistent :
                   *******************************************

   syscgssf.exe   syscgssi.exe : gaussjordan.
   syscinvi.exe   syscinvi.exe : inverse.


                    Symmetric matrices :
                    ******************

   syminvf.exe    syminvi.exe  : Inverses of symmetric matrices are symmetric :


                     Diagonal matrices :
                     *****************

   adiagaf.exe   adiagai.exe   :   Compare (Diag*A) and (A*Diag) 
  invdiagf.exe  invdiagi.exe   :   Inverse of diagonal matrices
  powdiagf.exe  powdiagi.exe   :   Power of diagonal matrices


                     Triangular matrices :
                     *******************

  triginvf.exe  triginvi.exe   :   Inverse of triangular matrices
   trigabf.exe   trigabf.exe   :   Multiply triangular matrices

                      Trace :
                      *****

  traplsbf.exe  traplsbf.exe   :   Trace(mA+B) = Trace(A)+Trace(B)
     trabf.exe     trabf.exe   :   Trace (AB)  = Trace(BA)





