Conservation of mass $-$ Reactor network. Consider the following network of well$-$mixed tank reactors ${?}^1.V^{}$ is flow rate and $c$ is concentration. They are in $\frac{m^3}{m}in$ and $m\frac{g}{m^3},$ respectively.

A contaminant is known to exist at different concentrations in the inlet streams. This contaminant acts as a homogeneous catalyst, and it can slightly affect the reactions in the reactors of this network. Develop a mass balance for this contaminant for every reactor. Put your equations in matrix form

$V_{{?}_{?}}{c}_{{?}_{?}}=m_{?}^{}$

where $V_{{?}_{?}}$ is a matrix that only contains flow rates, $c_{?}$ is a vector that only contains concentrations of the contaminant in the five reactors, and $m_{?}$ is a vector that only contains inlet mass flows of the contaminant. No need to substitute the values, a solution for $c_{?}$ is not expected at this point.