I have some hardship to conceive the intuitive meaning of a polyhedron which does not contain a line.
Suppose polyhedron $P = \{ x\in \mathbb{R^n : Ax \leq b, A\in \mathbb{R^{ m\times n }}} \}$ is not empty.
It is said that if P does not contain a line, then it has at least one extreme point, n independent active constraints exist and and therefore a basic feasible solution exists. Why is here the argument of a polyhedron not containing a line leading those following assertions? Thanks!