Overview of Week 1
Math 308 Section A, March 31, 1997
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Reading Assignment:
- Read Sections 1.1 and 1.2 for Wednesday, April 2.
- Read Sections 1.3 for Friday, April 4.
- Read Sections 1.4 for Monday, April 7.
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Homework Assignment:
- Section 1.1: Page 8, problems 1--6, 9, 16, 24, 25, 29, 33, 34
, 40, 41, 42.
Due Friday, April 4.
- Section 1.2: Page 19, problems 3--6, 13, 14, 22, 26, 33, 35,
36, 37, 49,
50(a). Due Friday, April 4.
- Section 1.3: Page 35, problems 8, 18, 21, 25, 28, 33, 34,
37, *49, *50a.
Due Monday, April 7.
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Vocabulary List:
- Section 1.1:
- linear equation
- m by n system of linear equations
- the solution set of an m by n system of linear equations
- equivalent systems of equations
- the three elementary operations
- scalar
- triangular systems of equations
- the three steps of Gaussian elimination
- Section 1.2:
- consistent and inconsistent systems of equations
- back--solving a triangular systems of equations
- overdetermined system
- Gauss--Jordan elimination
- Section 1.3:
- m by n matrix
- coefficient matrix
- augmented matrix
- the three elementary row operations
- row equivalence of matrices
- echelon form
- eduction to echelon form (4 steps for m by n matrices)
- reduced echelon form
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Key Concepts:
- Section 1.1:
- Linear systems of equations
- Equivalent solution sets
- The application of the three elementary operations yield
linear systems with
equivalent solution sets.
- Gaussian elimination yields an equivalent linear system in
triangular form that can then be solved by back--substitution.
- Section 1.2:
- An m by n system of linear equations has either (i) no
solution, (ii) infinitely many solutions, or (iii) a unique solution.
- Section 1.3:
- Matrix representation of linear systems
- Elementary row operations and reduction to echelon form
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Skills to Master:
- Reduction of a linear system to triangular form
(Gaussian elimination) and then
describing the solution set by back--substitution.
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Quiz:
- This quiz is based on the vocabulary words and homework associated with
Sections 1.1 and 1.2 of the text.