Huang solved via computer simulation the time-dependent concentration curves for a dechlorination and elimination reaction involving 10 species. The technique involved transformation of a coupled linear system of first-order differential equations into an uncoupled system via diagonalization of the reaction rate constant matrix, a technique admitted to suffer the shortcoming of the necessity of a full set of eigenvectors. In contrast, matrix exponential does not suffer from this restriction , . Moreover, it is easy to implement in MATLAB as e At can be calculated by the command expm(At) and postmultiplication by a column vector of initial concentrations produces the concentration vector at time t for the network (assuming the process starts at t = 0). As pointed out by Huang , the existing literature (e.g., , , ) provides theoretical treatments of matrix methods for chemical systems but lacks concrete computer implementations and sample concentration-time curves, which can be beneficial to both chemical engineers and chemists who desire simple and efficient programs dedicated to first-order kinetic analysis. This paper employs the matrix exponential technique, which can be compared to the diagonalization method . Before providing a general network description, we begin with kinetic equations for a system of three species and provide its solution in exact arithmetic.