# Math 2184: Linear Algebra I Section 10 Fall 2020

#### Contact Info Fall 2020

Office: Blackboard
Email: jaydaigle@gwu.edu

Office Hours:

• Monday 11 AM -12 noon
• Wednesday 5-6 PM
• Thursday 3-4 PM

#### Course Information

Lecture:

• TR 11:10 AM–12:25 PM
• on Blackboard

Textbook:

## Daily Assignments

Slides

Slides

#### October 13: Isomorphisms

Slides

• WeBWork due
• Check the solutions of mastery quiz 5.
• Watch the first five minutes of Essence of Linear Algebra, Chapter 13: Change of Basis to solidify some of the stuff with coordinate systems. We’ll come back and handle the rest of this video in a few weeks. (We could do the other half now, but I think it’s a bit more compelling if we have defined eigenvectors first. Feel free to watch the whole video and see if you agree.)

Slides

#### October 6: Bases and Coordinates

Slides

• Check the solutions of mastery quiz 4.
• The notes § 3.4
• LLM §4.4
• Beezer on Vector Representations (When Beezer writes $\mathbb{C}^n$ for the complex numbers, you can pretend he’s talking about $\mathbb{R}^n$ instead.)

Slides

Slides

Slides

#### September 22: Subspaces (and $LU$ factorizations)

Slides

• WeBWork due today
• Notes § 2.3
• LLM § 2.5
• Notes § 2.4
• LLM § 2.8 up until the “Basis for a subspace” section starts.
• You can read Beezer on Subspaces but he does things in a different order and will use fancy words you haven’t seen before. When he says “vector space” pretend he just said $\mathbb{R}^n$.
• Take a look at the solutions for quiz 2.

Slides

#### September 15: Applications of Linear Functions

Slides

• Mastery Quiz 2 Due at noon. Submit on Blackboard as one pdf file.

• Notes § 1.9. and §2.1
• LLM §1.10 and §2.1

#### September 10: Linear Transformations

Slides from Lecture

#### September 8: Solutions and independence of linear systems

Slides from lecture

• Mastery Quiz 1 Due at noon. Submit on Blackboard.
• (We won’t talk about bases for a couple of weeks, but I actually think that this presentation is a more sensible way to think about what they’re doing. And there are some good visualizations of how to think about span and linear independence.)
• LLM § 1.5 and 1.7
• Notes § 1.6 and 1.7
• Beezer “Homogeneous Systems of Equations”, “Linear Independence”, and “Linear Dependence and Spans”

#### September 3: Vectors and Matrix Equations:

Slides from lecture

• LLM §1.3-1.4
• Beezer “Vector Operations”, “Linear Combinations”, “Spanning Sets”, “Matrix Operations”, “Matrix Multiplication”
• Online Notes §1.4.-1.5.

#### September 1: Linear Equations and Row Echelon Form

Slides from lecture

• Read the introduction in the course notes.
• Watch Essence of Linear Algebra, Chapter 1 by 3Blue1Brown
• Read at least one of the following:
• Sections 1.1-2 of Lay, Lay, McDonald
• Sections “What is Linear Algebra?”, “Solving Systems of Linear Equations”, and “Reduced Row-Echelon Form” in Beezer
• Sections 1.1-3 of the online notes
• Optional/bonus: Watch this video on a technique called “Principal Component Analysis”. This is a sort of preview of what we want to be able to do by the very end of the course; it will mention a lot of ideas you haven’t been exposed to yet, but that you will see over the next few months.

## Course Goals

This is a standard first course in linear algebra. The main topics are: linear equations; matrix algebra and equations; subspaces and bases; vector spaces; eigenvalues and eigenvectors; determinants; orthogonality and least squares. This corresponds to Chapters 1–7 of Lay, Lay, and McDonald.

By the end of the course, students will acquire the following skills and knowledge:

• Students will be able to find echelon forms of matrices, find a basis for the column space, row space and null space of that matrix, and determine if that matrix is invertible.
• Students will be able to determine if a set of vectors is linearly independent.
• Students will be able to calculate the eigenvalues and eigenvectors of matrices.
• Students will be able to diagonalize a matrix and use the diagonalization techniques to solve problems in other areas of mathematics.

The course syllabus is available here.

## Mastery Quizzes

The topics for the quizzes are:

1. Systems of Linear Equations
2. Vector Equations and Spans
3. Linear Independence
4. Linear Transformations
5. Matrix Multiplication
6. Matrix Inverses
7. Subspaces
8. Basis and Dimension
9. Vector Spaces and Subspaces
10. Vector Space Linear Transformations
11. Bases and Coordinates
12. The Matrix of a Linear Transformation

## Tests

• Midterm due midnight on Tuesday, October 20
• Final Exam
• [Practice Final]
• [Solutions]

Graphing calculators will not be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.

## Textbook

The official textbook for Math 2184 is Linear Algebra and its Applications, Fifth Edition, by Lay, Lay, and McDonald (ISBN-13: 978-0321982384). I will be loosely following this book, and it will be very useful to have, but I will not be assigning problems out of it.

Another perfectly fine book is A First Course in Linear Algebra by Rob Beezer, which is available free online.