Linear Algebra

(Spring 2021)

This is an archive of the first 5 weeks of the linear algebra course I taught at Emory University in Spring 2021. I cross-posted all announcements and notes both here and on the Canvas page, but students much preferred Canvas and it got overwhelming to keep two websites up to date so I gave up posting here after the first half of the semester. I hope the incomplete information presented here is still somewhat helpful.



Please scroll all the way down for general information about the course, or click here for a PDF file with the course syllabus and policies.

Week 5 Day 3

Exam 1 will be held in class on Friday at our usual time. It covers sections 1.1-1.3 and 2.1-2.5.

Week 5 Day 2

In this class session, we will finish covering Section 2.5, review some material for the exam on Friday, and begin talking about transformations (Sec 2.2).

Class notes are now available here.

Zoom recording is available on Canvas.

Week 5 Day 1

In this class session, we will finish talking about Section 2.4: Matrix Inverses and start talking about Section 2.5: Elementary Matrices.

Class Notes are now available here.

Week 4 Day 3 (Lab):

Here's a copy of the worksheet we will use in lab:

https://www.dropbox.com/s/jqqg4xz0xocr1ru/M221-Sp21-Lab4-2.4%2C2.5.pdf?dl=0

Week 4 Day 2 (Rest Day!)

Wednesday, February 17th, is a university-wide rest day! Please take some rest!

Week 4 Day 1:

In this class session, we will go over Section 2.4: Matrix Inverses.

Class Notes are now available here.

Week 3 Day 3 (Lab):

Here's a copy of the worksheet we will use in lab:

https://www.dropbox.com/s/rfpi2xa4jfezouc/M221-Sp21-Lab2-2.2%2C2..pdf?dl=0

Week 3 Day 2:

In this class session, we will work on Section 2.3: Matrix Multiplication.

Before you come to class, you can think about the following problem:

Suppose that A and B are two m x n matrices such that Ax=Bx for EVERY n-vector x. What can you conclude about A and B?

Class Notes are now available here.

Week 3 Day 1

In this class session, we will begin Section 2.2: Matrix-Vector Multiplication.

Before you come to class, you can attempt to solve the following problem:

Write the general solution to the following system in parametric form

x − y − z + 3 w = 2

2 x − y − 3 z + 4 w = 6

x − 2 z + w = 4

Week 2 Day 2

In this class session, we will finish our discussion on Section 1.3, Homogenous Equations, and begin Chapter 2: Matrix Algebra.

Before you come to class:

Consider the following problem: Let A be an n x m matrix of rank r and consider the homogeneous system whose coefficient matrix is A. How many solutions does this system have? How many parameters are in the general solution?

Homework 1 is due on Friday, Feb 5th, on Gradescope at 1 PM.

Homework 2 is now available here. It's due a week from Friday on Gradescope at 1 PM.

Week 2 Day 1

In this class session, we will finish talking about the rank of a matrix, from Section 1.2. We will start Section 1.3: Homogenous Equations.

Recommended problems from Week 1:

If you'd like more practice from the contents of last week, you can look at the following problems from your book:

1.1.14-1.1.15, 1.1.18-1.1.20, 1.2.12, 1.2.16-1.2.22.

Week 1 Day 3: Lab

In this class session, we will go over the following worksheet together. If you'd like to print out a copy and bring it with you, you are welcome to download it here: https://www.dropbox.com/s/vtd6davzh641ita/M221-Sp21-Lab1-1.1%2C1.2.pdf?dl=0

Week 1 Day 2:

In this class session, we will cover the rest of Section 1.1, and start 1.2.

Before you come to class:

- Please consider the problem: Describe all solutions to 3x-y+2z=6 in parametric form in two different ways.

- Please fill out the Introductions! survey if you haven't already.

- Please confirm that you can access both Gradescope and Zoom chat! I will ask you to solve a problem in class and send it to me over Zoom chat in real-time.

Please submit by Friday, February 5th at 1 PM EST, over on Gradescope.

Week 1 Day 1:

In this class session, we will go over the syllabus, expectations for attending an in-person class during a pandemic, and Section 1.1 of our textbook.

Before you come to class:

  • Please carefully read over the syllabus file, make note of any questions you have, and come prepared to ask those questions in class.

  • At some point during Week 1, please complete the survey titled: Introductions! During class, I will ask you to tell us about yourself in a few sentences. Filling out the survey might help with coming up with an introduction beforehand :)

  • Here is a famous problem that uses linear algebra for you to think about if you are interested:

    • (The Hundred Fowls Problem.) One hen is worth 5 qian, one rooster 3 qian, and 3 chicks are worth 1 qian. If we bought 100 fowls with 100 qian, how many hens, roosters, and chicks did we buy?

Important note: Please don't feel discouraged if you cannot immediately solve the above problem. I haven't taught you anything yet! This is meant to give you a flavor of the kinds of things we will be talking about on Day 1.

Why linear algebra?

Syllabus.

Click here for a PDF file with the course syllabus and policies.

Course Websites.

  • All of the information presented here (and more) is also available on the Canvas site for this course.)

  • Other than Canvas, we will use Zoom and Gradescope in this class.

Textbook.

We will use the following textbook which is free to download:

The book consists of eleven chapters, we will cover most parts of the first eight chapters.

Miscellaneous Notes: