
 a) Write the chemical equation :

   a Cu**(2+) + b Cl**(-) + c SO[2] + d H[2]O -> e CuCl + f SO[4]**(-2) + g H**[+] 
   
 b) Write the list of the chemical elements.
 
         Cu :  a              =    e                        
         Cl :  b              =    e            
          S :  c              =    f            
          O : 2c + d          =   4f            
          H : 2d              =    g         
        +/- : 2a - b          = - 2f + g           


 c) Rewrite the list.

         Cu :  a - e          = 0 
         Cl :  b - e          = 0 
          S :  c - f          = 0
          O : 2c + d - 4f     = 0 
          H : 2d - g          = 0
        +/- : 2a - b + 2f - g = 0 



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

           a     b     c     d     e     f     g   
           ---------------------------------------
     Cu :  a                      -e               = 0 
     Cl :        b                -e               = 0 
      S :              c                -f         = 0
      O :             2c     d         -4f         = 0 
      H :                   2d                -g   = 0
    +/- : 2a    -b                      2f    -g   = 0 



 e) Complete the matrix :

           a     b     c     d     e     f     g   
           ---------------------------------------
     Cu : 1/1   0/1   0/1   0/1  -1/1   0/1   0/1  0/1 
     Cl : 0/1   1/1   0/1   0/1  -1/1   0/1   0/1  0/1  
      S : 0/1   0/1   1/1   0/1   0/1  -1/1   0/1  0/1 
      O : 0/1   0/1   2/1   1/1   0/1  -4/1   0/1  0/1  
      H : 0/1   0/1   0/1   2/1   0/1   0/1  -1/1  0/1 
    +/- : 2/1  -1/1   0/1   0/1   0/1   2/1  -1/1  0/1  


  f) This system has six rows, and seven values to find.
     ( a, b, c, d ,e, f, g ).
     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,   0,1,  1,1,      (a = 1/1)
       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,   0,1,   0,1,  -1,1,   0,1,  0,1, 
       0,1,   0,1,   2,1,   1,1,   0,1,  -4,1,   0,1,  0,1,  
       0,1,   0,1,   0,1,   2,1,   0,1,   0,1,  -1,1,  0,1, 
       2,1,  -1,1,   0,1,   0,1,   0,1,   2,1,  -1,1,  0,1,  


