Given a transportation problem in a Linear programming setting, we can draw a transportation array of dimension $m\times n$ where each cell corresponds to a variable. My doubt is given any random 3 cells, can we always get a basic feasible solution containing these 3 cells?
3 cells will be always LI in a transportation array and since the Basis is of dimension $m+n-1$, we can always extend these set of 3 cells to a basic set. Any set of basic cell can be solved to get a basic solution, But will this basic set always give us a basic feasible solution?