2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75357We analyze the representation of $A^{n}$ as a linear combination of $A^{j},\ 0\leq j\leq k-1,$ where $A$ is a $k\times k$ matrix. We obtain a first order asymptotic approximation of $A^{n}$ as $n\to\infty,$ without imposing any special conditions on $A.$ We give some examples showing the application of our results.14 pagesClassical Analysis and ODEsMSC-class: 15A15 (Primary) 34E05 (Secondary)text