Chemical Equation Balance using Linear Algebra

[michaelzip]

Hi.
Can you help me how to balance a chemical equation using linear algebra. I know how to do it on a piece of paper using the usual method of balancing. I just don't get the principle how to do it on the other method.

Please give me a step by step procedure on how to do it, the basic ones.

This is how far I have gone.
Ex: Fe + Cl2 = FeCl3

Set a variable for each
[A]Fe + Cl2 = [C] FeCl3

Count the number of coefficients
Fe: A = C
Cl: 2B = 3C

And I'm stuck with here. I don't know how will I get 2Fe + 3Cl2 = 2FeCl3 (the correct answer)

If you have a better/easy one, can you please post it here. I need to create a program that will balance a given equation. I don't have a problem anymore on extracting the values, chemical symbols, and coefficients. My professor gave me until May 10 to do this so I need a quick response.

Hoping you could help me,
Michael

[rubberman]

So, show how you solve this on paper. Then we can probably help you reflect that algorithm as pseudo code that you can fairly easily implement in a number of programming languages.

[michaelzip]

I will use the example above, Fe + Cl2 = FeCl3

Fe on left hand side has 1 atom, same with the right hand side so they are equal.
Cl on left hand side has 2 atoms, and 3 atoms on the right hand side.
To make Cl equal, I am adding 3 more Cl on left hand, and 2 on the right hand so that makes Fe + 3Cl2 = 2FeCl3.
They aren't balance yet since Fe on the left hand side has only 1 atom while Fe on the right hand side has 2 atoms. Now to make it balance, I am adding another two on the left, so that makes 2Fe + 3Cl2 = 2FeCl3