Linear Algebra

(Spring 2021)

Scroll all the way down for general information about the course. Click here for a PDF file with the course syllabus and policies.

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.