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In this paper, ignoring graph-theoretic tools, simple algebraic solutions are presented for the kinetic problems of the triangle, quadrangle and pentangle reactions with the help of Krylov and Vandermonde matrices. As far as we know at the time of writing, this is the first time for the cases of the quadrangle and pentangle reactions. Our solutions do not require diagonalizability and non-degenerate eigenvalues concerning the coefficient matrix of the first-order reaction network.

Simple algebraic solutions to the kinetic problems of triangle, quadrangle and pentangle reactions