I need help understanding the question.
Consider the polyhedron P = {x in R^n | Ax = b x => 0}, where A in R^mxn and b in R^m. Assume that any m columns of A are linearly independent.
(a) Suppose all the basic solutions are nondegenerate. Express the number of basic solutions in terms of m choose n
(b) Suppose that k basic solutions are degenerate, and each of these degenerate solutions have n+1 active constraints. Furthermore, all other basic solutions are nondegenerate. How many basic solutions are there?
(c) Suppose that there is one basic solution that is degenerate, and has n + 2 active constraints. Furthermore, all other basic solutions are nondegenerate. How many basic solutions are there?
for (a), I'm not sure if it is 2m choose n since there are 2m constraints and we need to ensure that there are n constraints to be tight.
Hope someone can enlighten me!
Thanks!
