COLLEGE OF SCIENCE,
ENGINEERING AND
TECHNOLOGY

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 signi-

cance; 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.

Textbook:

Linear Algebra and Its Applications plus New MyMathLab with Pearson eText

Access Card Package, 5/E –

Course 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.