I was dissatisfied with the method my teacher taught me to solve rate equations, where you're given experimental values for the concentrations of reactants, and the rate of reaction, which given by $$r = k\,[\ce{A}]^n\,[\ce{B}]^m\,\ldots,\tag{1}$$
as I thought the method wasn't very computational. Instead I rearranged the system of equations and was able to create a general formula to solve using matrices for any reaction
$$\ce{R_1 + R_2 + \ldots + R_n -> P[ ]}\tag{R1}$$ $$r = k\,[\ce{R_1}]^{N_1}\,[\ce{R_2}]^{N_2}\,\ldots\,[\ce{R_n}]^{N_n}\tag{2}$$
$$ \begin{pmatrix} \ln k \\ N_1 \\ N_2 \\ \vdots \\ N_n \end{pmatrix} = \begin{pmatrix} 1 & \ln_1R_1 & \ln_1R_2 & \cdots & \ln_nR_n \\ 1 & \ln_2R_1 & \ln_2R_2 & \cdots & \ln_nR_n \\ 1 & \ln_3R_1 & \ln_3R_2 & \cdots & \ln_nR_n \\ \vdots & & & \ddots & \\ 1 & \ln_nR_1 & \ln_nR_2 & \cdots & \ln_nR_n \\ \end{pmatrix}^{-1} \begin{pmatrix} r_1 \\ r_2 \\ r_3 \\ \vdots \\ r_n \end{pmatrix}\tag{3} $$
I'm wondering if this was an original formula for solving rate equations, and if the formula is obsolete as there must be different equations for rate of reaction dependent on temperature and pressure, which are just reduced to the constant $k$ in this equation.
