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1 vote

### Find which variables must be zero for non-negative solution to homogeneous linear equations

Some addition to @Alexey answer. There are many good solvers for LP (linear programming) problems; and if you are only dealing with some thousands of variables, open source solvers will suffice. ...
1 vote

### Find which variables must be zero for non-negative solution to homogeneous linear equations

If you are interested In an algorithmic solution I suggest the use of linear optimization. For example, say we have a system of equations: $$A\cdot x = 0$$ and we wish to check if $x_i$ always ...
1 vote

### Find which variables must be zero for non-negative solution to homogeneous linear equations

A simple approach is to use linear programming (LP). For each $j$, the problem is to maximize $x_j$ subject to $Ax=0$ and $x \ge 0$. For your example matrix $A$, the optimal objective value is $0$ ...

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