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In this paper we consider a linear homogeneous system of m equations in n unknowns with integer coefficients over the reals. Assume that the sum o the absolute values of the coefficients of each equation does not exceed k+1 for some positive integer k. We show that if the system has a nontrivial solution then there exists a nontrivial solution x = (x1,...,xn) ⊤ such that |xj| |xi| ≤ k n−1

Upper bounds on the magnitude of solutions of certain linear systems with integer coefficients