Review List For Exam #2 (November 14, 2007)

The Exam will cover material in Online Sections 8.1-8.5, 9.1-9.4.

Chapter 8; The Geometry of Vector Spaces

Definitions:

Affine combination, Convex combination (of vectors in Rⁿ).

Affine set, Affine hull, Flat, Homogeneous form of a vector in Rⁿ.

Affinely dependent set, Dimension of a flat, Barycentric coordinates.

Convex set, Convex hull, Hyperplane, Linear Functional.

Polytope, Polyhedron, Face, Vertex, Edge, Facet.

Minimal representation of a polytope, Extreme Point.

Theorems 1,3,4,5,12,13.14,16.

p.10,Ex.7; p.19,Ex.3,7; p.27,Ex.5; p.38,Ex.3, p.47,Ex.1.

Definitions:

Probability vector

Saddle Point

Value of a matrix game

Linear Programming Problem

Feasible Set of a LP problem

Slack Variable, Basic Feasible Solution

Simplex Method

Dual LP Problem

Theorem 3 (Fundamental Theorem for Matrix Games)

Theorem 6

Theorem 7 (The Duality Theorem)

p.15, Ex. 3,5,11 (do by the methods of 9.1 and 9.4); p.27, 1,3,7 (do by method of 9.2 and 9.3); p.42, 9,13; p.58, 1,11.