2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229706The aim of this note is to answer a question by Guoliang Yu of whether the group $EL_3(Z<x,y>)$, where $Z<x,y>$ is the free (non-commutative) ring, has any faithful linear representations over a field. We prove, in particular, that for every (unitary associative) ring $R$, the group $EL_3(R)$ has a faithful finite dimensional complex representation if and only if $R$ has a finite index ideal that has a faithful finite dimensional complex representation.8 pages, no figures; v3: a question about EL_2 from the first version is answeredGroup Theory20G15, 20H20text