**Course Prerequisites/Corequisites:** Math 242 or Equivalent.

**Course Description: **Introduces and provides models for application of the concepts of vector algebra. Topics include nite dimensional vector spaces and their geometric signicance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvector; and applications in science and engineering.

**Required Reading/Textbook:**
Linear Algebra and Its Applications plus New MyMathLab with Pearson eText, 5th Edition.

** Major Assignments/Exams**

- Homework
- Quizzes
- Exams
- Final Exam

**List of Discussion/Lecture Topics**:

- 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 Systems.
- 1.7 Linear Independence
- 1.8 Introduction to Linear Transformations.
- 1.9 The Matrix of a Linear Transformation.

- CHAPTER 2.Matrix Algebra
- 2.1 Matrix Operations
- 2.2 The Inverse of a Matrix
- 2.3 Characterizations of Invertible Matrices
- 2.8 Subspaces of Rn
- 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 Linearly Independent Sets; Bases
- 4.4 Coordinate Systems
- 4.5 The Dimension of a Vector Space
- 4.6 Rank

- 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 Eigenvalues

- OTHER TOPICS IF TIME PERMITS.

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