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# MAS 3105 — Linear Algebra — Syllabus

Co-Prerequisites: MAC 2283 or MAC 2313 and MGF 3301.

Course Description: The course meets for approximately 45 hours during a 15-week semester. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for three midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 75-minute time period.)

Text: Linear Algebra and Its Applications, 5th Edition, by Lay, Lay and McDonald

Course Content

Chapter 1: Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation $$Ax=b$$
1.5 Solution Sets of Linear Equations
1.6 Applications of Linear Systems (SKIP)
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering

Chapter 2: Matrix Algebra
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices (SKIP)
2.5 Matrix Factorization (SKIP)
2.6 The Leontief Input-Output Model (SKIP)
2.7 Applications to Computer Graphics (SKIP)
2.8 Subspaces of $$R^n$$
2.9 Dimension and Rank

Chapter 3: Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume and Linear Transformations

Chapter 4: Vector Spaces
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces and Linear Transformations
4.3 Linear Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains

Chapter 5: Eigenvalues and Eigenvectors
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvectors (SKIP)
5.6 Discrete Dynamical Systems (SKIP)
5.7 Applications to Differential Equations (SKIP)
5.8 Iterative Estimates for Eigenvalues (SKIP)

Chapter 6: Orthogonality and Least Squares
6.1 Inner Product, Length and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
6.5 Least-Squares Problems (SKIP)
6.6 Applications to Linear Models (SKIP)
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces (SKIP)

Pacing

1.1–1.5 (2 lectures)
1.7, 1.8, 1.9 (1 lecture each)

2.1, 2.2, 2.3 (2 lectures)
2.8, 2.9 (1 lecture each)

3.1, 3.2, 3.3 (3 lectures, with 1–2 lectures on 3.2)

4.1, 4.2 (1 lecture)
4.3, 4.4, 4.5, 4.6 (1 lecture each)
4.7 and 5.4 (Linear Transformation subsection) (1 lecture)

5.1, 5.2, 5.3, 5.4 (1 lecture each)

6.1, 6.2 (1 lecture)
6.3, 6.4, 6.7 (1 lecture each)

Total: 27 lectures