
                               You have seen : 
 
 a)  You must multiply m by three identity matrix,
     to eliminate all the values above the pivots.

        1/1 14/1 -16/1  19/1                        1/1  0/1  0/1  -19/1  
  m =   0/1  1/1  13/1  11/1     example :   mID1 = 0/1  1/1  0/1  -11/1
        0/1  0/1   1/1  11/1                        0/1  0/1  1/1  -11/1
        0/1  0/1   0/1   1/1                        0/1  0/1  0/1    1/1

  mID1 : to eliminate all the values above the fourth pivot.
  mID2 : to eliminate all the values above the third  pivot.
  mID3 : to eliminate all the values above the second pivot.
 
                            Can you do that in one step ?
                           ===========================

    Multiply  mID3 by mID2 by mID1, in this order.

         mID = (mID3 * mID2) * mID1.

               And then mutiply mID by m.  

                1/1  0/1  0/1  0/1  
    mID * m  =  0/1  1/1  0/1  0/1
                0/1  0/1  1/1  0/1
                0/1  0/1  0/1  1/1

   The work must be do without swap two rows.
   -----------------------------------------