2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155566Let $\tilde{K}_{3,n}$, $n\geq 3$, be the simple graph obtained from $K_{3,n}$ by adding three edges to a vertex part of size three. We prove that if $H$ is a hyperplane of a 3-connected matroid $M$ and $M \not\cong M^*(\tilde{K}_{3,n})$, then there is an element $x$ in $H$ such that the simple matroid associated with $M/x$ is 3-connected.19 pages, 3 figures, submitted to Advances in Applied MathematicsCombinatorics05B35text