M308 F Matrix Algebra

Course Summary

This is a first course in linear algebra. It is truly surprising how ubiquitous linear algebra is throughout math and sciences: from cryptography to graph theory, from machine learning to research mathematics. Whether you are an aspiring computer scientist, mathematician, physicist, biologist or engineer, the techniques we will learn in this class are a fundamental component of your studies. Topics include solving linear systems of equations, span and linear independence of vectors, linear transformations, inverses, subspaces, change of basis, the determinant function, eigenvalues and eigenvectors, and diagonalization.

CAUTION! This course is a 4 week version of a 10 week course. During a 10 week version of this course, a typical student spends 8-20 hours per week (including lecture hours). DO NOT take this course unless you are able to commit to 20-40 hours of work per week.

Information

Syllabus

Academic Honesty Pledge

Instructor: Josh Southerland

Office Hours: via Zoom

• Monday - Thursday: 4:30-5:30 (tentatively)

Office: Padelford (PDL), C-552

Contact: j s o u t h e r AT u w . e d u

Additional help is available outside of class and office hours at CLUE. Visit their website to find out more about online assistance.

Homework: Webassign & Conceptual Problems

For homework, you will need to use Webassign and Gradescope. Professor Taggart how generously typed up instructions for how to use Webassign. You can find them here. When you log into Webassign, use this link (or google "uw Webassign" to get this page). Conceptual problems will require solutions, and you will need to upload these solutions to Gradescope.

Technology Requirements

All lectures in this course have been pre-recorded, with certainexceptions. However, starting the second week of the class, I will be available on Zoom during the usual lecture hours. Additionally, office hours, quizzes and exams will be on Zoom. For additional Zoom and technology policies, refer to the syllabus. As an alternative, you have access to Ebru Bekyel's lectures from last quarter (see below). In general, this means you will need the following for this class.

• A laptop or phone that will allow you to participate in Zoom video conference calls
• Regular internet access
• Browser that can access Gradescope, Webassign, Canvas, and Catalyst
• Gradescope Account
• Webassign Account
• The ability to upload PDFs of written work (for example: phone apps that convert images to pdfs)

Exams & Quizzes

Practice Quiz: Friday, June 26

Covers 1.1, 1.2, 2.1.

Solutions

Quiz 1: Monday, July 6

Review Session

Covers 2.2, 2.3, 3.1 (and you need to understand techniques from 1.1-2.1)

Solutions

Quiz 2: Friday, July 10

Review Session

Covers 3.2, 3.3, 4.1 (and you need to understand techniques from 1.1-3.1)

Solutions

Quiz 3: Friday, July 17

Review Session

Covers 4.2, 4.3, 4.4, 5.1/5.2 (and you need to understand techniques from 1.1-4.1)

Solutions

Final Exam: Wednesday, July 22

Review Session:Conc. Ch 6 #7f, Spring 2020 #1c, Diagonalizability and Geom., Fall 2019 #3, Spring 2020 #2, Fall 2019 #6

Solutions

Course Schedule with Lecture Notes and Recordings

Week	Monday	Tuesday	Wednesday	Thursday	Friday
Jun 22	Lectures Live Lecture 1: Logistics and Starting 1.1 Lecture 2: Section 1.1 Lecture Notes 1.1	Homework Upload Academic Honesty Pledge	Lectures Lecture 3: Section 1.2 Lecture 4: Section 1.2, 2.1 Lecture 5: Section: 2.1 Lecture Notes 1.2 2.1	Homework Webassign 1.1 1.2 Conceptual C1: Ch.1 #3, #5ab, #9 Additional Assistance Office Hours, 4/7/20: Webassign 1.1 #5, Conceptual #9, start of #5 Office Hours, 4/9/20: Conceptual #5	Practice Quiz: 9:40-10:05 Lectures Lecture 6: Section: 2.2 Lecture 7: Section: 2.2 Lecture Notes 2.2
Jun 29	Lectures Lecture 8, 4/15/20: Section: 2.3 Lecture 9, 4/17/20: Section: 2.3 (through 35:50) Lecture Notes 2.3	Homework Webassign 2.1 2.2 2.3 Chapter 2 Videos (3Blue1Brown) Vectors Span and Linear Independence Additional Assistance Office Hours, 4/14/20: Webassign 2.2 #11 (through 33:20)	Lectures Lecture 10: Section: 3.1 Lecture 11: Section: 3.1 + Technical Difficulties :( Lecture 12: Section: 3.1, through 33:45 Lecture Notes 3.1	Homework Webassign 3.1 Conceptual C2: Ch.2 #2,4,6,7 Additional Assistance Office Hours, 4/14/20: Conceptual Ch.2 #4 Notation (starting at 33:20) Office Hours, 4/16/20: Conceptual Ch.2 #6, #7cef Office Hours, 4/28/20: Webassign 3.1 #9, #4, #10a (through 24:30)	Holiday!
Jul 6	Quiz 1: 9:40-10:05 Lectures Lecture 12: Section: 3.2, starting at 33:45 Lecture 13: Section: 3.2 + Q about last exercise in notes Lecture 14: Section: 3.3 Lecture Notes 3.2 3.3	Homework Webassign 3.2 3.3 Conceptual C3: Ch.3 #2,5,7,9 Chapter 3 Videos (3Blue1Brown) Linear Transformations and Matrices Matrix Multiplication as Composition 3D Linear Transformations Additional Assistance Office Hours, 4/28/20: (starting at 24:30) Conceptual #2a,d, #7 Office Hours, 4/30/20: Ch3 Conceptual #5abcd, Webassign 3.2 #5; Conceptual #9 Office Hours, 5/5/20: Webassign 3.3 #8, #5 (through 44:50)	Lectures Lecture 15: Section: 4.1 Lecture 16: Section: 4.2 Lecture 17: Section: 4.2, (through 18:30) Lecture Notes 4.1 4.2	Homework Webassign 4.1 4.2 Conceptual C4: Ch.3 #12,13; Ch.4 #2 Additional Assistance Office Hours, 5/5/20: (start at 44:50) Conceptual Ch. 4 #2a + new techniques for thinking about #2 Office Hours, 5/7/20: Ch. 4 Conceptual #2d, Webassign 4.1 #4, General Subspace Question, Ch. 3 Conceptual #4	Quiz 2: 9:40-10:05 Lectures Lecture 17: Section: 4.3, (starting at 18:30) Lecture 18: Rank-Nullity Intuition + Review Lecture Notes 4.3
Jul 13	Lectures Lecture 19: Section 4.4 Lecture 20: Section 5.1/5.2 (Day 1) Lecture Notes 4.4 5.1, 5.2	Homework Webassign 4.3 4.4 Conceptual C5: Ch.4 #5,7,8ab,9,10 Chapter 4 Videos (3Blue1Brown) Inverse Matrices, Column Space and Null Space Nonsquare matrices as Transformations between Dimensions Change of Basis If you hear references to the "determinant being non-zero", just think the matrix is invertible, or that the matrix must have linearly independent column vectors. Additional Assistance Office Hours, 5/12/20: Webassign 4.3 #10, Ch. 4 Conc. #7, Win 2020 #3f, Ch. 4 Conc #8b, Bonus, Remark on Row/Null Space Office Hours, 5/14/20: Ch. 4 Conceptual #10 (1:18:45-1:42:45); Ch. 4 Conceptual #9a (2:07:00-2:15:45)	Lectures Lecture 21: Section 5.1/5.2 (Day 2) Lecture 22: Section 6.1 Lecture 23: Sections 6.1, through 34:25 Lecture Notes 5.1, 5.2 6.1	Homework Webassign 5.1 5.2 6.1 Conceptual C6: Ch.5 #2,5abd,8,9; Ch. 6 #4 Chapter 5 Videos (3Blue1Brown) The Determinant Additional Assistance Office Hours, 5/19/20: Ch. 5 Conceptual #5d, #7 Office Hours, 5/20/20: Webassign 5.1 #12, Ch. 5 Conceptual #9bde, Midterm 2 #3 Office Hours, 5/26/20: Webassign 6.1 #8, #10cd, Ch. 5 Conceptual #2, #8 Office Hours, 5/28/20: Ch. 6 Conceptual #4 (through 1:20:00)	Quiz 3: 9:40-10:05 Lectures Lecture 23: Sections 6.2, starting at 34:25 Lecture 24: Section 6.2 Lecture Notes 6.2
Jul 20	Review Day! (live on Zoom) Review Day Recording Extras Old review days Review Day 1, 6/01/20: Kahoot!, Determinant fact, #3 Lee Aut'18 Review Day 2, 6/03/20: Kahoot!, #7 Goeckner Aut'18, Commutativity question + Aut '19 Bonus	Homework Webassign 6.2 Conceptual C7: Ch.6 #3,5,6,7,8 Chapter 6 Videos (3Blue1Brown) Eigenvalues and Eigenvectors Additional Assistance Office Hours, 5/28/20: Ch. 6 Conceptual #5 (start at 1:22:50) Office Hours, 6/02/20: Webassign 6.2 #8, Ch. 6 Conceptual #8, #3be	Final Exam: 9:40-11:50 Use the Zoom Lecture link		Extra lecture (just for fun!) Page Rank Lecture, 6/05/20: Google's Page Rank Algorithm!

Alternative Lecture Recordings: Ebru Bekyel

• 1.1
• 1.2
• 2.1
• 2.2
• 2.3
• 2.3 Unifying Theorem
• 3.1
• 3.1 - Geometry
• 3.2
• 3.3
• 3.5 (Markov Chains!)
• 4.1
• 4.2
• 4.3
• 4.4
• 5.1
• 5.2
• 5.3 (Cramer's Rule)
• 6.1
• 6.2

Exam Archives & Concept Checklists

Midterm 1

• Midterm 1 Concept Checklist
• Math 308 Exam 1 Archive (You may ignore all problems asking about linear transformations.)
• Review Session Video, 4/21/20: Win '20 3b, Bonus Aut '19, Levinson #3, Thomas #3, Bonus Win '20, Conceptual 1 #7(c), Thomas #4
• Midterm 1 Fall 2019
• Midterm 1 Fall 2019 Solutions
• Midterm 1 Winter 2020
• Midterm 1 Winter 2020 Solutions
• Midterm 1 Spring 2020 (open book)
• Midterm 1 Spring 2020 Solutions
• Review Video of Spring 2020 Midterm 1, 5/2/20: All solutions

Midterm 2

• Midterm 2 Concept Checklist
• Archive 1 (You may ignore questions asking you to change the basis, compute a determinant, or compute eigen-anything.)
• Midterm 2 Review Session, 5/14/20: Roven '18 1e, 1d, 3b; Subspace Question; Ch. 4 Conceptual #10; Chapter 4 Checklist Question; Ch. 4 COnceptual #9a; Ch.3 Conceptual #8; Ch. 4 Conceptual #1; Midterm 2 Fall 2019 #2; Midterm 2 Winter 2020 #2
• Midterm 2 Fall 2019
• Midterm 2 Fall 2019 Solutions
• Midterm 2 Winter 2020
• Midterm 2 Winter 2020 Solutions
• Midterm 2 Spring 2020 (open book)
• Midterm 2 Spring 2020 Solutions
• Review Video of Spring 2020 Midterm 2 Solutions, 5/25/20: All solutions + alternative solutions

Final Exam

• Final Exam Concept Checklist
• Final Exam: Archive 1 (You may ignore problems that ask about orthogonality and least squares regression. You do not need to worry about complex-valued eigenvalues, you only need to know how to work with real-valued eigenvalues.)
• Final Review Session, 6/07/20: Lui Aut '17 #1d, Won Aut '18 #4, Viray Aut '18 #11, Ch. 5 Checklist question, Won Aut '18 #1g, Thomas Win '18 #4b, Lui Aut '17 #3bc, Viray Aut '18 #12, Goeckner Aut '18 #6bc, Liu Aut '17 #5d, Aut '19 #4b
• Final Autumn 2019
• Final Autumn 2019 Solutions
• Final Spring 2020
• Final Spring 2020 Solutions

Other Materials

• Chapter 1 Conceptual Problems
• Chapter 2 Conceptual Problems
• Chapter 3 Conceptual Problems
• Chapter 4 Conceptual Problems
• Chapter 5 Conceptual Problems
• Chapter 6 Conceptual Problems
• Chapter 2 Videos: Vectors, Span and Linear Independence
• Chapter 3 Videos: Linear Transformations and Matrices, Matrix Multiplication as Composition, 3D Linear Transformations
• Chapter 4 Videos: Inverse Matrices, Column Space and Null Space, Nonsquare matrices as Transformations between Dimensions, Change of Basis NOTE: If you hear references to the "determinant being non-zero", just think the matrix is invertible, or that the matrix must have linearly independent column vectors.
• Chapter 5 Video: The Determinant
• Chapter 6 Video: Eigenvalues and Eigenvectors
• Cross Product Review (Loveless)
• Scalar Equation of a Plane