Question: Balance the chemical equation using Linear Algebra.

Answer: In order to balance the chemical equations, we need to find the five unknowns (ab,c,d,e).

Since the number of chemical elements are conserved, we know that:

we need to solve the following linear system.

This system of equations can easily be solved with Maple.

> with(Student[LinearAlgebra]):
> A := Matrix([[1, 1, 0, -1, 0, 0],
		[1, 2, 0, 0, -1, 0],
		[0, 0, 2, -4, -2, 0]]):
> ReducedRowEchelonForm(A)

According to maple, we can reduce the linear system to:

According to the above equation, we don’t have a unique solution. However, we know that the linear system will have a solution where

Since we know that (where ), we can add additional constraints to our linear system. If we look at the above equations, it is easy to see that the following constraint must hold:

Using the linear system and the above constraint, we find the following solutions…

…
…

As you can see, there is still an infinite amount of solutions for this chemical equations. Some can be reduced, however majority of the equations can’t be reduced

Question: Balance the chemical equation using Linear Algebra.

I finally finished my first math related webapp! The webapp is designed to solve a system of linear equations using Gaussian elimination with partial pivoting.

If you find any bugs or have any feature requests, please email at bugz@jkwiens.com.