
 * Solve this system :                                 (ca1.c)

  1/1   3/1  -2/1   0/1   2/1   0/1   0/1
  2/1   6/1  -5/1  -2/1   4/1  -3/1  -1/1
  0/1   0/1   5/1  10/1   0/1  15/1   5/1
  2/1   6/1   0/1   8/1   4/1  18/1   6/1

 * The gaussjordanF() function give :

  1/1   3/1   0/1   4/1   2/1   0/1   0/1
  0/1   0/1   1/1   2/1   0/1   0/1   0/1
  0/1   0/1   0/1   0/1   0/1   0/1   0/1     < zero row
  0/1   0/1   0/1   0/1   0/1   1/1   1/3


 * Eliminate the zero row.                              (ca2.c) 
 * The leading variables are (pivot = 1) :
  
   x1          x3                    x6

 [1/1] 3/1   0/1   4/1   2/1   0/1   0/1       
  0/1  0/1  [1/1]  2/1   0/1   0/1   0/1               
  0/1  0/1   0/1   0/1   0/1  [1/1]  1/3

  
 * The  free  variables  are (pivot = 0) :
  
        x2         x4    x5    
  
  1/1  3/1   0/1   4/1   2/1   0/1   0/1       
  0/1 [0/1]  0/1   0/1   0/1   0/1   0/1
  0/1  0/1   1/1   2/1   0/1   0/1   0/1
  0/1  0/1   0/1  [0/1]  0/1   0/1   0/1
  0/1  0/1   0/1   0/1  [0/1]  0/1   0/1               
  0/1  0/1   0/1   0/1   0/1   1/1   1/3

  * We assign a value at the free variables : 

        x2=r        x4=s  x5=t    
                                            r    s    t 
  1/1   3/1   0/1   4/1   2/1   0/1   0/1
  0/1 [1/1]   0/1   0/1   0/1   0/1   0/1  [1/1] 
  0/1   0/1   1/1   2/1   0/1   0/1   0/1
  0/1   0/1   0/1  [1/1]  0/1   0/1   0/1       [1/1]  
  0/1   0/1   0/1   0/1  [1/1]  0/1   0/1            [1/1]
  0/1   0/1   0/1   0/1   0/1   1/1   1/3


  * Now you can compute the general solution :

  1/1   3/1   0/1   4/1   2/1   0/1   0/1   0/1   0/1   0/1
  0/1  [1/1]  0/1   0/1   0/1   0/1   0/1  [1/1]  0/1   0/1
  0/1   0/1   1/1   2/1   0/1   0/1   0/1   0/1   0/1   0/1
  0/1   0/1   0/1  [1/1]  0/1   0/1   0/1   0/1  [1/1]  0/1
  0/1   0/1   0/1   0/1  [1/1]  0/1   0/1   0/1   0/1  [1/1]
  0/1   0/1   0/1   0/1   0/1   1/1   1/3   0/1   0/1   0/1
