 # Say I have a system of linear equalities and inequalities with integer coefficients in n variables, glutynowy44 2022-07-01 Answered
Say I have a system of linear equalities and inequalities with integer coefficients in n variables, and let ${R}^{n}$ be the space of all possible solutions. I know that $\stackrel{\to }{0}$ is a solution.
Is there any efficient algorithm to check if there are any other solutions but zero? In other words, given a linear optimization problem, is there a way to check if the feasible region is a point?
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I think the following is pretty much it:
Bring the problem into canonical form (where all variables are greater than zero) and checking for maximum of the function $f\left(x\right)=\left(1,1,...,1\right)\ast x$ using any LP solver.
Since no variable can be negative, the maximum can only be greater than 0 iff there's no unique solution.

We have step-by-step solutions for your answer! Holetaug
You can use some LP solver to find the $minf$ and $maxf$ for some non zero linear function $minf=maxf=0$ if and only if 0 is the unique point in your feasible region

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