
 a) Write the chemical equation :

   a LiBH[4] + b BF[3] -> c B[2]H[6] + d LiBF[4]
   
 b) Write the list of the chemical elements.
 
         Li :  a                =   d        | a = d -> a - d = 0 -> 0 = 0 
          B :  a +  b           =  2c + d    | This line is not useful. 
          H : 4a                =  6c
          F : 3b                =  4d


 c) Rewrite the list.

         Li :  
          B :  a +  b - 2c - d  = 0
          H : 4a - 6c           = 0
          F : 3b - 4d           = 0 


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

           a     b     c     d    
           -------------------
     Li :  
      B :  a     b   -2c    -d  = 0
      H : 4a         -6c        = 0
     F :        3b         -4d  = 0 


 e) Complete the matrix :

           a     b     c     d     
           --------------------
     Li :  
      B :  1/1   1/1  -2/1  -1/1   0/1
      H :  4/1   0/1  -6/1   0/1   0/1
      F :  0/1   3/1   0/1  -4/1   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)
           1,1,  1,1, -2,1,  0,1, -1,1,
           4,1,  0,1, -6,1,  0,1,  0,1,
           0,1,  3,1,  0,1, -4,1,  0,1, 
 




