I have a question that might or might not be trivial for experts from the linear programming world.
We have a system of linear equations that we want to solve: $A\cdot x=0$, with the constraint that all variables are non-negative: $x_i \geq 0 ~\forall i$.
The system is underdetermined, i.e. $A$ has more columns than rows, more variables than equations.
Question: How do we determine which $x_i$ can never be positive (i.e. are zero) in the solution space. That means, determine those $x_i$ for which $ x_i = 0$ for any solution.