***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

*This course was previously MATH 2331*

Text:  Linear Algebra and Its Applications (6th Edition) [Hardcover], David C. Lay. ISBN­: 9780135851258 (effective Spring 2023)

Prerequisite: Credit for or concurrent enrollment in MATH 2414.

Course Description: Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors.

Upon successful completion of this course, students 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.

[Additional course curriculum details: 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; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvector; and applications in science and engineering.]

Course Syllabus:

(1) Linear Equations in Linear Algebra

1.1  Systems of Linear Equations
1.2  Row Reduction and Solution Sets of Linear Systems
1.3  Vector Equations
1.4  The Matrix Equation Ax =b
1.5  Solutions Sets of Linear Systems
1.7  Linear Independence
1.8  Introduction to Linear Transformations
1.9  The Matrix of a Linear Transformation

(2) Matrix Algebra

2.1  Matrix Operations
2.2-3  The Inverse of a Matrix and Characterizations of Invertibility
2.4  Partitioned Matrices
2.8 Subspaces of R^n
2.9 Dimension and Rank

(3) Determinants

(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 Vector Space
4.6  Rank
*4.7  Change of Basis
*4.9  Applications to Markov Chains


(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
*5.6-8  Applications


(6) Orthogonality and Symmetric Matrices

6.1  Inner Product, Length, and Orthogonality
6.3  Orthogonality and Projections
6.4  The Gram-Schmidt Process
6.5  Least-Squares Problems

(7) Symmetric Matrices and Quadratic Forms

*7.1  Diagonalization of Symmetric Matrices
*7.2  Quadratic Forms
*7.3  The Singular Value Decomposition

*Sections are optional, as time permits

Grading: Please consult your instructor's syllabus regarding any and all grading guidelines.

Justin Dart Jr. Center Accommodations:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at https://www.uh.edu/accessibility/ for more information.

UH CAPS

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