Math 2121 (Fall 2026)

Overview

Welcome to the homepage for Math 2121: Linear Algebra!

Send questions for an instructor to emarberg@ust.hk or maymin@ust.hk.
Send questions about grades to your TA.

Check out the syllabus here.

Lecture notes

Our lectures this semester will be held at the following times:

L1: Tuesdays & Thursdays, 16:30 - 17:50
L2: Tuesdays & Thursdays, 15:00 - 16:20
L3: Mondays, 13:30 - 14:50, & Fridays, 9:00 - 10:20

For lecture locations consult the university registry.

Lecture notes will be posted on this site. Try to read these before each class.

Week 1:

Lecture 1: Systems of linear equations [slides]
Lecture 2: Row reduction to echelon form [slides]
Practice Problem Set #1

Week 2:

Lecture 3: Vectors in Euclidean space [slides]
Lecture 4: Matrix-vector products, linear independence [slides]
Practice Problem Set #2

Week 3:

Lecture 5: More linear independence, linear transformations [slides]
Lecture 6: One-to-one and onto functions [slides]

Week 4:

Lecture 7: Matrix operations, matrix multiplication [slides]
Lecture 8: Invertible functions and invertible matrices [slides]

Week 5:

Lecture 9: Subspaces, null and column space [slides]
Lecture 10: Dimension and rank [slides]

Week 6:

Lecture 11: Introduction to determinants [slides]
Lecture 12: Properties of determinants [slides]

Other resources

The following is our primary textbook:

Linear Algebra and its Applications, 6th edition, by D. Lay, S. Lay, and J. McDonald

Some other online resources:

This is a great YouTube channel dedicated to linear algebra topics.
Linear Algebra Done Right by Axler is a useful supplementary textbook.
Khan academy has many good instructional videos on linear algebra.
Check out HKUST professor Jeffrey Chasnov's Matrix Algebra for Engineers on Coursera.

From time to time, we will show some interactive Pluto notebooks in class using the Julia programming language. Using these programming tools is completely optional and not necessary for the course. If interested, you may access the relevant files below.

Notebook 1: Solving linear systems [code]
Notebook 2: Random walks and matrix-vector multiplication [code]

Grades

Grades will be computed as follows:

5%: online homework assignments
5%: offline homework assignments
30%: midterm examination
60%: final examination

Homework

There are two components to the homework in this course: online and offline.

We will have weekly online homework assignments. Here are the relevant logistics:

Online homework will be submitted using WebWork.
These assignments will be due on Fridays at midnight, starting September 11.

There is also a weekly offline component to the homework. Here are the relevant logistics:

A list of practice problems will be posted each week with the lecture notes.
You must solve some of these probems and submit your answers by hardcopy (see instructions).
These assignements will be due on Mondays at midnight, starting September 14.

For both parts of the homework, no deadline extensions will be granted and no late submissions will be accepted. However, we will omit your lowest online score and lowest offline score from final grade computations. This means you can skip any one week of homework with no penalty.

Midterm

We will have a 2 hour, out-of-class midterm. The date and time are TBD.

The midterm will be closed book, closed notes, with no calculators or other electronic devices allowed.

Final

We will have a cumulative 3-hour final exam at the end of the semester.

This exam will also be closed book, closed notes, with no calculators or other electronic devices allowed.

Schedule

The following is a tentative course outline, with reading assignments from the textbook.

Week 1: Linear systems, row reduction to echelon form (reading: Sections 1.1-1.2)
Week 2: Vectors, matrix equations, linear independence (reading: Sections 1.3-1.5, 1.7)
Week 3: Linear independence, linear transformations (reading: Sections 1.7-1.9)
Week 4: Matrix multiplication, the inverse of a matrix (reading: Sections 2.1-2.3)
Week 5: Subspaces, bases, dimension (reading: Sections 2.4, 2.8-2.9)
Week 6: Determinants (reading: Sections 3.1-3.2)
Week 7: Vector spaces, midterm (reading: Sections 4.1-4.6)
Week 8: Eigenvectors, and eigenvalues (reading: Section 5.1)
Week 9: Similarity and diagonalisable matrices (reading: Sections 5.2-5.4)
Week 10: Complex eigenvalues, properties of eigenvalues (reading: Sections 5.5, 6.1)
Week 11: Inner products, orthogonality, and projections (reading: Sections 6.1-6.3)
Week 12: Gram-Schmidt process, least-squares problems (reading: Sections 6.4-6.6)
Week 13: Symmetric matrices, SVDs (reading: Sections 7.1, 7.4)