LSC-CyFair Math Department

Catalog Description

Introduces and provides models for application of the concepts of vector algebra. Topics include finite dimensional vector spaces and their geometric significance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; metrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvectors; and applications in science and engineering. Additional topics may include constructing proofs using definitions and basic theorems.

Course Learning Outcomes

The student will:

• Be able to solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
• Be able to carry out matrix operations, including inverses and determinants.
• Demonstrate understanding of the concepts of vector space and subspace.
• Demonstrate understanding of linear independence, span, and basis.
• Be able to determine eigenvalues and eigenvectors and solve problems involving eigenvalues.
• Apply principles of matrix algebra to linear transformations.
• Demonstrate application of inner products and associated norms.

Contact Hour Information

Credit Hours:  3
Lecture Hours:  3
Lab Hours:  0
External Hours:  0
Total Contact Hours:  48

Prerequisites

MATH 2414 (Calculus II);
College level readiness in reading and writing

Required Materials

Textbook:

Lay, Lay, McDonald; Linear Algebra and its Applications, 6th ed.;  Pearson
ISBN Number for Hard Copies of Required MyMathLab Access Codes: 9780135851159
Loose-Leaf Copy of Text with MyMathLab Access: 9780136858140

Calculator:

Calculators may be required for some assignments/assessments at the discretion of the instructor. Refer to class syllabus for details.
Cell phones and other internet-connected devices may not be used as calculators. Calculators may be cleared before tests.

Textbook Sections

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 Equations
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
2.5 Matrix Factorizations

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
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis

Chapter 5.  Eigenvalues and Eigenvectors
5.1  Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization

Chapter 6.  Orthogonality and Least Squares
6.1 Inner Product, Length and Orthogonality
6.2 Orthogonal Sets