Before revision:  We present an algorithm to decide the feasibility of an instance in time O(n^2) and we show that  even the smallest feasible solution can be computed in strongly polynomial time O(n^3).
After revision:  We present an algorithm to decide the feasibility of an instance in time O(n^2) and we show that if it exists even the smallest feasible solution can be computed in strongly polynomial time O(n^3).