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 $\overrightarrow{0}$ 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?

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?