Matrix Formulation of Reaction Rates

Consider a system with N chemical components undergoing a set of M reactions. Define the A x M matrix of stoichiometric coefficients as 

There is a row in this matrix for each of the N components and a column for each of the M reactions. Multiply w by the vector (M x 1 matrix) of reaction rates, 0l, to obtain the vector (Af x 1 matrix) of component reaction rates  

Using this notation, we can write the design equations for a batch reactor in very compact form  

Consider a constant-volume batch reaction with the following set of reactions  

These reaction rates would be plausible if B were present in great excess, say as water in an aqueous reaction. Equation 2.44 can be written out as 

---