Given an $m \times n$ real matrix $Y$, an unbounded set $\mathcal{T}$of parameters $t =( t_1, \ldots,t_{m+n})\in\mathbb{R}_+^{m+n}$ with $\sum_{i = 1}^m t_i =\sum_{j = 1}^{n} t_{m+j} $ and $0$|Y_i\q - p_i| $|q_j| (here $Y_1,\ldots,Y_m$are rows of $Y$).We show that for any $\varepsilon0$ such that forany drifting away from wallsunbounded $\mathcal{T}$, any $\varepsilon Our results extend those of several authors beginning with the work of Davenportand Schmidt done in late 1960s. The proofs rely on a translation of the probleminto a dynamical one regarding the action of a diagonal semigroup onthe space $\SL_{m+n}(\mathbb R)$/$SL_{m+n}(\mathbb Z)$.