
 a) Write the chemical equation :

   a C[8]H[18] + b O[2] -> c CO[2] + d H[2]0
   
 b) Write the list of the chemical elements.
 
          C :  8a               =   c        
          H : 18a               =  2d   
          O :  2b               =  2c + d
   


 c) Rewrite the list.

          C :  8a -  c          =  0        
          H : 18a - 2d          =  0   
          O :  2b - 2c - d      =  0

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

           a     b     c     d
           -------------------
     C :  8a          -c         =  0
     H : 18a                -2d  =  0
     O :        2b   -2c    - d  =  0


 e) Complete the matrix :

           a     b     c     d     
           --------------------
     C :  8/1   0/1  -1/1   0/1  0/1
     H : 18/1   0/1   0/1  -2/1  0/1
     O :  0/1   2/1  -2/1  -1/1  0/1




  f) This system has three rows, and four values to find.
     ( a, b, c, d ).
     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,  1,1,    (a = 1/1)
           8,1,  0,1, -1,1,  0,1,  0,1,
          18,1,  0,1,  0,1, -2,1,  0,1,
           0,1,  2,1, -2,1, -1,1,  0,1,
 




