
 a) Write the chemical equation :

    a FeS[2] + b O[2] + c H[2]O -> d FeSO[4] + e H[2]SO[4]

   
 b) Write the list of the chemical elements.
 
         Fe :  a           =  d                            
          S : 2a           =  d +  e       
          O : 2b + c       = 4d + 4e           
          H : 2c           = 2e            

 c) Rewrite the list.

         Fe :  a -  d           = 0            
          S : 2a -  d -  e      = 0            
          O : 2b +  c - 4d - 4e = 0           
          H : 2c - 2e           = 0            


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

           a     b     c     d     e    
           --------------------------
     Fe :  a                -d         = 0
      S : 2a                -d    -e   = 0            
      O :       2b     c   -4d   -4e   = 0           
      H :             2c         -2e   = 0            

 e) Complete the matrix :

           a     b     c     d     e    
           --------------------------
     Fe :  1/1   0/1   0/1  -1/1   0/1  0/1
      S :  2/1   0/1   0/1  -1/1  -1/1  0/1            
      O :  0/1   2/1   1/1  -4/1  -4/1  0/1           
      H :  0/1   0/1   2/1   0/1  -2/1  0/1            



  f) This system has four rows, and five values to find.
     ( a, b, c, d ,e).
     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,  1,1,            
           1,1,   0,1,   0,1,  -1,1,   0,1,  0,1,
           2,1,   0,1,   0,1,  -1,1,  -1,1,  0,1,            
           0,1,   2,1,   1,1,  -4,1,  -4,1,  0,1,           
           0,1,   0,1,   2,1,   0,1,  -2,1,  0,1,            








