question:I'm given the reaction $\displaystyle Na_2S_4O_6+H_2O_2 --> Na_2SO_4 +H_2O + H_2SO_4$ and I need to find the coefficient in front of each term so that all the variables are balanced. Na is one variable.

work:I take the homogeneous linear equations which are

[html]2a-2c=0

4a-c-e=0

6a+2-4c-d-4e=0

2b-2d-2e[/html]So that gives the matrix

$\displaystyle

\left(

\begin{array}{ccccc}

2 & 0 & -2 & 0 & 0 \\

4 & 0 & -1 & 0 & -1 \\

6 & 2 & -4 & -1 & -4 \\

0 & 2 & 0 & -2 & -2 \\

\end{array} \right) $

2 0 -2 0 0

4 0 -1 0 -1

6 2 -4 -1 -4

0 2 0 -2 -2

when I plug this into matlab I get

$\displaystyle \left| \begin{array}{ccccr}

1 & 0 & 0 & 0 & \frac{-1}{3} \\

0 & 1 & 0 & 0 & \frac{-2}{3} \\

0& 0 & 1 & 0 & -\frac{1}{3} \\

0 & 0 & 0 & 1 & -\frac{1}{3} \end{array} \right|.$

1.0000 0 0 0 -0.3333

0 1.0000 0 0 -2.3333

0 0 1.0000 0 -0.3333

0 0 0 1.0000 -1.3333

but now I'm not sure how to interpret the results. Since I have 4 equations and 5 unknowns, doesn't that mean one of the coefficients can be any number?