In a closed system the reacting species interconvert but do not leave the system. Therefore the amounts of different species in the system would be bound by a conservation rule.

>A simple example:
$$\ce{A -> B}$$

Here the conservation rule would be: $\ce{A + B = constant}$, which says that at any point of time during the reaction the sum of the amount of both the species would be constant.

> A more complex example
$$\ce{2A -> B}$$

Here, the conservation rule would be: $\ce{A + 2B = constant}$.

Let's take a more complex system:
> $$\begin{align}
\ce{A &-> B} \\
\ce{2B &-> C} \\
\ce{C &-> D + E} \\ 
\ce{2A + C &-> F}
\end{align}$$

From empirical analysis I can deduce that the conservation rule would be: $$\ce{A + B + 2C + D + E + 4F = constant}$$

However, I am not able to deduce a mathematical equation that gives these co-efficients. I assume that the stoichiometry matrix may give a clue but I am not sure. The stoichiometry matrix for the above system is:

$$\mathbf{S}=\begin{bmatrix}
-1 & 0 & 0 & -2 \\
1 & -2 & 0 & 0 \\
0 & 1 & -1 & -1 \\
0 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}$$

This is relatively easier to figure out empirically as there is only one starting reactant (A). For reaction systems with multiple starting reactants (as shown below), the deduction of conservation rule(s) becomes even more difficult.

$$\ce{aA + bB -> cC + dD}$$
The problem seems quite elementary but I am not able to solve it. Am I missing something obvious?