
 a) Write the chemical equation :

   a C[6]H[12]O[6] + b I[3]**(-) + c OH**(-) -> d C[6]H[11]O[7]**(-) + e H[2]O + f I**(-)
   
 b) Write the list of the chemical elements.
 
         C :  6a                    =  6d                        
         H : 12a + c                = 11d + 2e           
         O :  6a + c                =  7d + e            
         I :  3b                    =   f            
       +/- :  -b - c                =  -d - f          


 c) Rewrite the list.

         C :  6a - 6d                =  0                        
         H : 12a +  c - 11d - 2e     =  0        
         O :  6a +  c -  7d -  e     =  0            
         I :  3b -  f                =  0            
       +/- :  -b -  c +   d +  f     =  0          




 d) Write the list of the chemical elements in a matrix :

           a     b     c     d     e     f     
           -------------------------------
     C :  6a               -6d             =  0                        
     H : 12a           c  -11d   -2e       =  0        
     O :  6a           c   -7d    -e       =  0            
     I :        3b                     -f  =  0            
   +/- :        -b    -c     d          f  =  0




 e) Complete the matrix :

           a     b     c     d     e     f        
           -------------------------------
     C :  6/1   0/1   0/1  -6/1    0/1  0/1   0/1                      
     H : 12/1   0/1   1/1 -11/1   -2/1  0/1   0/1     
     O :  6/1   0/1   1/1  -7/1   -1/1  0/1   0/1          
     I :  0/1   3/1   0/1   0/1    0/1 -1/1   0/1          
   +/- :  0/1  -1/1  -1/1   1/1    0/1  1/1   0/1


  f) This system has five rows, and six values to find.
     ( a, b, c, d ,e, f).
     If the system is consistent, it will have many solutions.

     To find a solution, I must give a value, to a coefficient.
     I have chosen to write a = 1/1.

       1,1,  0,1,   0,1,   0,1,   0,1,  0,1,  1,1,    (a = 1/1)
       6,1,  0,1,   0,1,  -6,1,   0,1,  0,1,  0,1,                      
      12,1,  0,1,   1,1, -11,1,  -2,1,  0,1,  0,1,     
       6,1,  0,1,   1,1,  -7,1,  -1,1,  0,1,  0,1,          
       0,1,  3,1,   0,1,   0,1,   0,1, -1,1,  0,1,          
       0,1, -1,1,  -1,1,   1,1,   0,1,  1,1,  0,1,            

