Overview of Week 2
Math 208 Section A, October 4, 2021
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Reading Assignment:
- Sections 1.1, 1.2 and 2.1 of text, due Monday 10/4.
- Sections 2.2 of text due Wednesday 10/6.
- Section 2.3, due Friday 10/8.
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- Section 1.1, due 10/01/21
- Section 1.2, due 10/04/21
- Section 2.1, due 10/06/21
- Section 2.2, due 10/11/21
- Section 2.3, due 10/13/21
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Conceptual Problems:
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Vocabulary List:
- Chapter 1:
- linear equation
- linear systems of equations
- Gaussian elimination
- Triangular systems
- echelon form
- free variables
- augmented matrices
- elementary row operations
- reduced echelon form
- Gauss-Jordan elimination
- homogeneous linear systems
- Chapter 2:
- vectors and their properties
- linear combinations of vectors
- solutions of linear systems as linear combinations of vectors
- the linear span of a collection of vectors
- when is a given vector an element of the linear span of a vectors
- the relationship between linear span and echelon form
- matrix vector multiplication
- matrix equations Ax=b
- linear independence of vectors
- linear span and linear independence
- homogeneous systems
- algebra of matrix vector multiplication
- particular plus homogeneous solutions
- The Unifying Theorem - Version 1. (Theorem 2.21)
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Key Concepts:
- Chapter 1:
- Linear systems of equations
- Gaussian elimination as a method to attain echelon form
- augmented matrices
- Echelon form and the solution of a linear system
- Gauss-Jordan elimination and reduced echelon form
- Chapter 2:
- linear combinations and linear span
- the relationship between linear span and echelon form
- the relationship between linear independence and echelon form
- particular plus homogeneous solutions
- The Unifying Theorem - Version 1
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Skills to Master:
- Chapter 1
- Gaussian elimination, reduction to echelon form, and reduction to reduced echelon form
- solving linear systems by parametrizing the free variables
- Chapter 2
- Solving matrix equations
- writing the solution set of a linear system as a linear combination of vectors
- Checking linear independence and the relationship to echelon form
- computing particular and homogeneous solutions