(untitled) (Journal of Computational Mathematics, 2021)
This paper deals with a system of ordinary differential equations with known conditions associated with a given matrix. By using analytical and computational methods, the generalized inverses of the given matrix can be determined. Among these are the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse. In particular, a new insight is provided into the finite algorithms for computing the generalized inverse and the inverse.