Welcome to the homepage for Math 2121: Linear Algebra!

- Send questions for the instructor to
**emarberg@ust.hk**. - Send questions about grades to your TA.

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

- L1:
**Tuesdays & Thursdays, 15:00 - 16:20**, in CYT G010 - L2:
**Tuesdays & Thursdays, 10:30 - 11:50**, in CYT G010

New lecture notes will be posted each Friday. 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 Problems

- Lecture 3: Vectors in Euclidean space [slides]
- Lecture 4: Matrix-vector products, linear independence [slides]
- Practice Problems

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

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

- (no lecture on Tuesday due to public holiday)
- Lecture 9: Subspaces, null and column space [slides]
- Practice Problems

- Lecture 10: Dimension and rank [slides]
- Lecture 11: Introduction to determinants [slides]
- (no graded Practice Problems this week)

- Lecture 12: Properties of determinants

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.

Grades will be computed as follows:

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

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
**Mondays at midnight**, starting**9 September**.

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.
- Each week, choose
**four**practice problems and write down solutions. - You can earn extra credit by solving more practice problems. See the instructions.
- These assignments will be due on
**Wednesdays at midnight**, starting**11 September**.

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

- Date:
**October 17** - Time:
**8pm to 10pm** - Location:
- LTB for section L1
- LTC for section L2

**make note of your tutorial**and report to the correct room.

The midterm will cover

Review problems and practice exams:

- Some review problems with solutions.
- Practice Midterm from 2018 [solutions]
- Practice Midterm from 2019 [solutions]
- Practice Midterm from 2021 [solutions]
- Practice Midterm from 2022 [solutions]

This exam will also be closed book, closed notes, with no calculators or other electronic devices allowed. More information about the final exam, including the time, location, and practice materials, will be posted here later.

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)