A ring R is a weakly stable ring provided that aR + bR = R implies that there exists $y;{in};R$ such that $a;+;by;{in};R$ is right or left invertible. In this article, we characterize weakly stable rings by virtue of $2{ imes}2$ invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any $A;{in}GL_2(R)$, there exist two invertible lower triangular L and K and an invertible upper triangular U such that A = LUK, where two of L, U and K have diagonal entries 1. Related results are also given. These extend the work of Nagarajan et al.