## Overview of 407 Week 1

• Review notes for Math 308: Due Friday, October 2.
• Class Notes: Section 1: Introduction: pages 1-11: Due Wednesday, October 7.

• #### 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.