2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145564We consider n by n real matrices whose entries are non-degenerate random variables that are independent but non necessarily identically distributed, and show that the probability that such a matrix is singular is O(1/sqrt{n}). The purpose of this note is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non degenerate random variables.to be published in the Proc. Amer. Math. SocProbability15A52, 60C05text