Overview of 407 Week 1

Reading Assignment:
 Review notes for Math 308: Due Friday, October 2.
 Class Notes: Section 1: Introduction: pages 111: Due Wednesday, October 7.
Homework Assignment:

Vocabulary List:
 Math 308 Review:
 m by n systems of linear equations
 Gaussian elimination
 echelon form
 dot product
 orthogonal vectors
 singular matrices
 subspace
 basis and dimension
 internal representation of a subspace
 external representation of a subspace
 the 4 fundamental subspaces associated with a matrix
 rank and nullity
 Notes: Introduction:
 decision variable
 linear function
 linear inequality
 the solution set of a system of linear inequalities
 objective function
 linear programming
 explicit and implicit linear constraints
 the 4 steps in LP modeling
 Graphical solutions to LPs in two variables
 standard form
 optimal value
 optimal solution
 feasible solution
 infeasible LP
 unbounded LP
 sensitivity analysis
 optimal value function
 the marginal value of a resource (shadow prices)
 the dual of an LP in standard form
 the Weak Duality Theorem

Key Concepts:
 Math 308 Review:
 Linear systems of equations
 Gaussian elimination as a method to attain echelon form
 Echelon form and the solution of a linear system
 Computing the inverse of a nonsingular matrix.
 Subspaces and their representations: internal and external
 Properties of the 4 fundamental subspaces associated with a matrix.
 block structured matrices
 Notes Introduction:
 What is an LP?
 Graphical solutions to LPs in two variables.
 What is LP standard form?
 The Weak Duality Theorem

Skills to Master:
 Gaussian elimination, reduction to echelon form
 Computing the inverse of a nonsingular matrix
 manipulation of block structured matrices
 Graphical solution of LPs in two variables
 LP modeling
 transformation of an LP to standard form

Quiz:
Friday, October 2.
 This quiz is based on the vocabulary words and homework associated with
the
Math 308 review
material.