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.
Linear Algebra and Its Applications plus New MyMathLab with Pearson eText
Access Card Package, 5/E –
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.