# Math 2121 (Fall 2021)

### Overview

Welcome to the homepage for Math 2121: Linear Algebra!

• Send questions for the instructor to emarberg@ust.hk.
Check out the syllabus here.

### Lecture notes

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

• L1: Wednesdays & Fridays, 13:30 - 14:50, online through Zoom Meeting in Canvas
• L2: Mondays & Wednesdays, 12:00 - 13:20, in LTG

New lecture notes will be posted each Friday. Try to read these before class.

Week 1:

Week 2:
• Lecture 3: Vectors in Euclidean space
• Lecture 4: Matrix-vector products, linear independence
Week 3:
• Lecture 5: Linear independence, linear transformations
• Lecture 6: One-to-one and onto functions
Week 4:
• (No lecture on Wednesday due to holiday)
• Lecture 7: Matrix operations, matrix multiplication
Week 5:
• Lecture 8: Invertible functions and matrices
• (No lecture on Friday/Monday due to holiday)
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
Week 11:
• Lecture 19: Orthogonal vectors, orthogonal projections
• Lecture 20: Orthogonal projections, Gram-Schmidt process
Week 12:
Week 13:

### Programming tools

I will be showing some interactive Pluto notebooks in class using the Julia programming language.

You can view these notebooks as static HTML pages, but you are strongly encouraged to install Julia and Pluto in order to run and modify the code in each notebook yourself. This may be useful for exploring ideas, checking problems, and future reference. However, using these programming tools is completely optional and not necessary for the course.

### Other resources

The following is our primary textbook:

• Linear Algebra and its Applications, 5th edition, by D. Lay, S. Lay, and J. McDonald

Some other online resources:

Grades will be computed as follows:

• 10%: homework assignments, weighted equally
• 30%: midterm examination
• 60%: final examination

### Homework

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

• Homework will be submitted online using WeBWorK.
• Assignments will be due at midnight each Friday.
• If you need extra time, be sure to request this before the deadline.
• The first homework assignment will be due on 9 September.
The graded homework assignments are only a bare minimum of preparation for keeping up with the course. It is a good idea to do extra problems, such as the odd numbered exercises in the sections of the textbook corresponding to each lecture. These problems have solutions at the end of the textbook.

### Midterm

We will have a 2-hour, out of class midterm.
• Date: Tuesday, 26 October 2021
• Time: 7:00PM-9:00PM
• Location:
• LTJ (for section L1)
• Room 2303 (for tutorial T2A)
• Room 2404 (for tutorial T2B)
• Room 2405 (for tutorial T2C)
Email the instructor right away if you need special arrangements, due to a time conflict or being unable to come to campus.

The midterm will cover Lectures 1-12 and HW 1-6.

Review problems and practice exams:
Here are solutions to the midterm.

### Final

We will have a 3-hour final examination at the end of the term
• Date: Saturday, 18 December 2021
• Time: 12:30PM-3:30PM
• Location: S H Ho Sports Hall
The format will be similar to the midterm.
The exam will be cumulative, covering all lectures and homework.

Review problems:
Practice exams:
Here are solutions to the final exam.

### 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)