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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