  # Math 250: Linear Algebra (3)

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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