Overview of Week 1
Math 308M, September 25, 2013
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Reading Assignment:
- Read Linear Systems from Your Past, due Friday, Sept 27.
- Read Sections 1.1 and 1.2, due Friday, Sept 27.
- Read Sections 1.3 for Monday, Sept 30.
- Read Sections 1.4 for Wednesday, Oct 2.
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Homework Assignment:
- Linear Systems from Your Past:
All problems due Oct 2.
- Section 1.1:
Sec. 1.1: 11, 12, 14, 15, 32, 38, 39,
due Oct 2.
- Section 1.2:
Sec. 1.2: 6, 8, 14, 23, 26, 36, 50,
due Oct 2.
- Section 1.3:
Sec. 1.3: 2, 3,
due Oct 2.
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Vocabulary List:
- Section 1.1:
- linear equation
- solution to a linear equation
- m by n system of linear equations
- solution set of an m by n system of linear equations
- consistent and inconsistent system of equations
- and m by n matrix
- the coefficient matrix for a linear system of equations
- the augmented matrix for a linear system of equations
- equivalent systems of equations
- the three elementary operations
- scalar
- row equivalence of matrices
- the three steps of Gaussian elimination
- Section 1.2:
- Echelon form
- Reduced echelon form
- The 6 step process of reduction to reduced echelon form for an $(m\times n)$ matrix.
- The 3 step process of solving a linear system of equations.
- a general solution to a linear system of equations
- a particular solution to a linear system of equations
- Gauss--Jordan elimination
- Section 1.3:
- the 3 solution possibilities for a linear system of equations
- homogeneous linear systems
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Key Concepts:
- Section 1.1:
- Linear systems of equations
- Equivalent solution sets
- matrices, coefficient matrices, augmented matrices
- The application of the three elementary operations yield
linear systems with
equivalent solution sets.
- Gaussian elimination yields an equivalent linear system in
triangular form.
- Gauss-Jordan elimination
- Section 1.2:
- Echelon fom and reduced echelon form
- reduction to echelon form
- Section 1.3:
- consistent and inconsistent systems
- homogeneous systems
- An m by n system of linear equations has either (i) no
solution, (ii) infinitely many solutions, or (iii) a unique solution.
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Skills to Master:
- Reduction of a linear system to triangular form
(Gaussian elimination) and
reduction to reduced echelon form (Gauss-Jordan elimination).
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Quiz: