  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.