Suppose that we have a basic feasible solution of the system Ax = b, x ≥ 0 with basis B. Suppose that z k – c k > 0 and x k is introduced into the basis and x Br is removed from the basis. Denote the new basis by B’. Show algebraically that after pivoting:
a. The column under x is (B’) -1 a j .
b. The column under the right hand side is (B’) -1 b.
c. The new cost row is composed of (c B ) (B’) -1 a j – c i
