Linear Algebra

Fall 2026, University of Houston.

Course information

Meets — Tue & Thu, 10am–11:30am

Location — TU2 211

Office hours — Tue & Thu, 11:30am–1pm, & by appointment

Textbook — Linear Algebra and Its Applications, by David C. Lay, Steven R. Lay, and Judi J. McDonald (ISBN: 9780135851258).

Announcements

Quiz 6will cover 4.1 and 4.2. Pay attention to Ex. 11 in 4.1.

Lecture notes

1.1Systems of linear equations
1.2Row reduction and echelon forms
1.3Vector equations
1.4Matrix equations
1.5Solution sets of linear systems
1.7Linear independence
1.8Linear Transformations
1.9The Matrix of a Linear Transformation
2.1Matrix Operations
2.2Inverses
2.4Partitioned Matrices
2.8Subspaces
2.9Dimension and Rank
3.1Determinants
3.2Properties of Determinants
3.3Cramer's Rule
4.1Vector Spaces and Subspaces
4.2Examples of Subspaces and Linear Transformations
4.3Linearly Independent Sets and Bases

Homework

The following homework problems are from the 6th edition of the textbook.

Section 1.111, 21, 23
Section 1.24, 11, 19
Section 1.31, 5, 9, 11, 33, 35
Section 1.41, 3, 10, 11, 15, 22, 36
Section 1.51, 5, 19, 41, 42
Section 1.75, 9, 45
Section 1.83, 9, 17, 38
Section 1.92, 5, 21, 37, 44
Section 2.11, 2, 10, 11, 32
Section 2.21, 5, 31, 41
Section 2.323, 41
Section 2.47
Section 2.81, 2, 8, 15, 20, 31
Section 2.91, 7, 13, 29
Section 3.11, 9, 11, 12, 25-30
Section 3.215-20, 45
Section 3.35, 6, 11, 13, 32
Section 4.13, 11, 42
Section 4.26, 24, 52
Section 4.427, 28
Section 4.52, 9, 41, 42