
 a) Write the chemical equation :

   a Cu[2]S + b H**(+) + c NO[3]**(-) ->  d Cu**(2+) +  e NO +  f S[8] +   g H[2]O

   
 b) Write the list of the chemical elements.
 
         Cu : 2a           =  d                        
          S :  a           = 8f            
          H :  b           = 2g           
          N :  c           =  e            
          O : 3c           =  e + g         
        +/- :  b - c       = 2d           


 c) Rewrite the list.

         Cu : 2a -  d      = 0         
          S :  a - 8f      = 0    
          H :  b - 2g      = 0     
          N :  c -  e      = 0    
          O : 3c -  e -  g = 0       
        +/- :  b -  c - 2d = 0    


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

           a     b     c     d     e     f     g   
           ---------------------------------------
     Cu : 2a                -d                     = 0                
      S :  a                           -8f         = 0
      H :        b                            -2g  = 0
      N :              c          -e               = 0
      O :             3c          -e           -g  = 0
    +/- :        b    -c   -2d                     = 0


 e) Complete the matrix :

           a     b     c     d     e     f     g   
           ---------------------------------------
     Cu :  2/1   0/1   0/1  -1/1   0/1   0/1   0/1   0/1
      S :  1/1   0/1   0/1   0/1   0/1  -8/1   0/1   0/1
      H :  0/1   1/1   0/1   0/1   0/1   0/1  -2/1   0/1
      N :  0/1   0/1   1/1   0/1  -1/1   0/1   0/1   0/1
      O :  0/1   0/1   3/1   0/1  -1/1   0/1  -1/1   0/1
    +/- :  0/1   1/1  -1/1  -2/1   0/1   0/1   0/1   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 g = 1/1.

           2,1,  0,1,  0,1, -1,1,  0,1,  0,1,  0,1,  0,1,  
           1,1,  0,1,  0,1,  0,1,  0,1, -8,1,  0,1,  0,1,  
           0,1,  1,1,  0,1,  0,1,  0,1,  0,1, -2,1,  0,1,  
           0,1,  0,1,  1,1,  0,1, -1,1,  0,1,  0,1,  0,1,  
           0,1,  0,1,  3,1,  0,1, -1,1,  0,1, -1,1,  0,1,  
           0,1,  1,1, -1,1, -2,1,  0,1,  0,1,  0,1,  0,1, 
           0,1,  0,1,  0,1,  0,1,  0,1,  0,1,  1,1,  1,1,           (g = 1/1) 


