  We present an approach of taking a linear weighted Average of N given
scalars, such that this Average is zero, if and only if, all N scalars are
zero. The weights for the scalars in this Average vary asymptotically with
respect to a large positive real. We use this approach with a previous result
on Asymptotic Linear Programming, to develop an O(M^4) Algorithm that decides
whether or not a system of M Linear Inequalities is feasible, and, whether or
not any desired subset of the variables in this system, is permitted to have a
non-trivial solution.
