(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Balance the following Chemical Equation

(x1)KMnO4+(x2)MnSO4+(x3)H2O->(x4)MnO2+(x5)K2SO4+(x6)H2SO4

2. Relevant equations

Here is the matrix I came up with but it seems to be flawed but I am unable to see what i am doing wrong

1 0 0 0 -2 0 (K)

0 1 0 -1 0 0 (Mn)

4 4 1 -2 -4 -4 (O)

0 1 0 0 -1 -1 (S)

0 0 2 0 0 -2 (H)

Each column corresponds to the amount of each element in each compound.

This is the reduced row echelon form of the matrix

1 0 0 0 0 -1/3

0 1 0 0 0-7/6

0 0 1 0 0 -1

0 0 0 1 0-7/6

0 0 0 0 1 -1/6

I seem to be missing the free variable I need to solve this problem

3. The attempt at a solution

The answer i come up with is

X1=(1/3)

X2=(7/6)

X3=(1)

X4=(7/6)

X5=(1)

and here is the problem for I only get five answers and not the six that i need to balance the equation. Can anyone point me in a direction or say what I am doing wrong any help will be appreciated thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Balancing Chemical Equations with Linear Algebra

**Physics Forums | Science Articles, Homework Help, Discussion**