Overview of Week 1
Math 407 Section A, September 24, 2012
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Reading Assignment:
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Homework Assignment:
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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
- Note, Section 1: Introduction
- decision variable
- linear function
- linear inequality
- the solution set of a system of linear inequalities
- linear programming
- objective function
- explicit and implicit linear constraints
- standard form
- optimal value
- optimal solution
- feasible solution
- infeasible LP
- unbounded LP
- sensitivity analysis
- 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.
- Note, Section 1:
- What is an LP?
- What is LP standard form?
- The Weak Duality Theorem
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Skills to Master:
- Gaussian elimination, reduction to echelon form
- Computing the inverse of a nonsingular matrix.
- Graphical solution of LPs in two variables
- LP modeling
- transformation of an LP to standard form
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Quiz:
- This quiz is based on the vocabulary words and homework associated with
the Math 308 review material through the material on block structured
matrices but not including the final section on block structured Gaussian elimination.