Matrix Solution to the Coupled Rate Equation

Appendix A. Matrix Solution to the Coupled Rate Equation (5.2) 

The set of coupled equations (5.2) can be readily solved using matrix methods. The advantage of this approach is that it can easily be generalized to treat any number of coupled first-order (or pseudo-first-order) rate equations. For simplicity consider a two-step process and define a column vector constructed from the concentrations 

From the results of matrix algebra it is known that a transformation matrix T can always be constructed to generate a new vector 

The rules for determining A and T are well known A is found by solving the algebraic equation which is formed by expanding the determinant 

Introducing (5A.4) into (5A.5) we find another relation between dYjdt and X 

---