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Math 310: Applied Linear Algebra

Course Prerequisites

Grade of C or better in MATH 181 (Calculus II)

Course Description

Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, diagonalization of symmetric matrices, applications to differential equations and Markov processes. Credit is not given in both MATH 310 and MATH 320 (Linear Algebra I).

Calculators not permitted on exams or quizzes.

Credit Awarded

3 hours


  • The courses uses a free textbook that can be found here.
    A First Course in Linear Algebra, K. Kuttler, Lyryx Version 2023-A. (publisher: Lyryx with Open Texts)


  • The course uses the MyOpenMath platform for online homework and quizzes. No purchase for this is required.

Linear Algebra Internet Resources

Sample Exams and Material Heading link

Course Schedule Heading link

The following is a typical 15-week Fall or Spring semester schedule for MATH 310. During the Summer sessions, the schedule is condensed into 8 weeks.
Sections labelled * are optional and may be omitted by the instructor.
Sections Topics
Week 1
Systems of linear equations
Row reduction and echelon Forms
Week 2

Solutions of linear Equations
Rank and homogeneous systems
Applications of linear systems
Week 3

Matrix operations
Matrix inverses
Week 4
Further properties of the inverse of a matrix
LU Decomposition
Week 5

Review and Midterm 1
Week 6

Applications of the determinant
Vectors, length and dot product
Week 7
Spanning set of vectors
Linear independence
Subspaces and Bases
Week 8
Column Space and null Space
Rank-nullity theorem
Week 9

Review and Midterm 2
Week 10

Orthogonal projections
Least squares solutions
Week 11

Linear transformations
Eigenvectors and eigenvalues
Week 12
Week 13
Markov chains
Orthogonal Diagonalization
Week 14
Singular Value Decomposition
Week 15
Applications of Singular Value Decomposition
Week 16
Finals' Week
Final Exam