I have a linear underdetermined system $Ax = b$ with constraints $0 \le x \le 1$. Matrix $A \in \mathbf{R}^{n \times m}$ with $n < m$, elements of which are either $0$ or $1$, and sum of each column equals to $2$.
Is there any analytical way to check if there is a solution at all? If yes, how can we get any of the solutions from the feasible set?