MATH 2331 - Linear Algebra - University of Houston
Skip to main content

MATH 2331 - Linear Algebra

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

Text:  Linear Algebra and Its Applications (5th Edition) [Hardcover], David C. Lay. ISBN­: 9780321982384

Prerequisite: Credit for or concurrent enrollment in MATH 1432.

Course Description: Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors. *Note: TCCNS Equivalent: MATH 2318


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

3.1  Introduction to Determinants
3.2  Properties of Determinants, the Determinant and Invertibility
3.3  Cramer's Rule, Volume, and Linear Transformations
*Permutation Matrices (not in text)

(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


CSD 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 The Center for Students with DisABILITIES (CSD) website at for more information.

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.



Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.