Let be a polyhedron in defined by the constraints for , , and .
In the solutions of an exercise, the following is mentioned:
"Since the first constraints are linearly independent, they correspond to a basic solution of the system which, a priori, may be feasible or infeasible. This solution is obtained by replacing inequalities with equalities and computing the unique solution of this linear system."
So I am quite confused about this:
1) Why does "linear independent constraints" imply that "basic solution"?
2) Is a basic solution not always feasible?