Overview of 407 Week 1
Math 407, January 7, 2019
-
Reading Assignment:
- Review notes for Math 308: Due Friday, Jan. 11.
- Class Notes: Section 1: Introduction: pages 1-11: Due Monday, Jan. 14.
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
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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, Jan. 11.
- This quiz is based on the vocabulary words and homework associated with
the
Math 308 review
material.