## 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.

## Information

**Instructor:** Josh Southerland

**Office Hours:** via Zoom

- Tuesday: 4:30-5:30
- Thursday: 3:30-4:30

**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 will be done via Zoom. For additional Zoom and technology policies, refer to the syllabus. All lectures will be recorded live and a link to the video uploaded to the course website; however, the turnover time between the live recording and posting may be in excess of 2 days. As an alternative, you will also have links to Ebru Bekyel's lectures as the come available, and all lectures notes.

- 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

**Midterm 1:** Wednesday, April 22

**Midterm 2:** Friday, May 15

**Final Exam:** Monday, June 8

## Lecture Notes

## Lecture Recordings

#### Josh (Section O)

- Lecture 1, 3/30/20: Course Introduction, section 1.1
- Lecture 2, 4/1/20: Section 1.1
- Lecture 3, 4/3/20: Section 1.2
- Lecture 4, 4/6/20: Section 1.2, 2.1
- Office Hours, 4/7/20: Webassign 1.1 #5, Conceptual #9, start of #5
- Lecture 5, 4/8/20: Section: 2.1
- Office Hours, 4/9/20: Conceptual #5
- Lecture 6, 4/10/20: Section: 2.2
- Lecture 7, 4/13/20: Section: 2.2
- Office Hours, 4/14/20: Webassign 2.2 #11, Notation on Conceptual #4a, + other Qs
- Lecture 8, 4/15/20: Section: 2.3
- Office Hours, 4/16/20: Conceptual #6, Conceptual #7cef, + other Qs
- Lecture 9, 4/17/20: Section: 2.3, Questions about Midterm, Kahoot
- Lecture 10, 4/20/20: Section: 3.1
- Review Session, 4/21/20: Win '20 3b, Bonus Aut '19, Levinson #3, Thomas #3, Bonus Win '20, Conceptual 1 #7(c), Thomas #4
- Lecture 11, 4/24/20: Section: 3.1 + Technical Difficulties :(
- Lecture 12, 4/27/20: Section: 3.1, 3.2
- Office Hours, 4/28/20: Webassign 3.1 #9, #4, #10a; Conceptual #2a,d, #7
- Lecture 13, 4/29/20: Section: 3.2 + Q about last exercise in notes
- Office Hours, 4/30/20: Ch3 Conceptual #5abcd, Webassign 3.2 #5; Conceptual #9
- Lecture 14, 5/1/20: Section: 3.3
- Review of Midterm 1, 5/2/20: All solutions
- Lecture 15, 5/4/20: Section: 4.1
- Office Hours, 5/5/20: Webassign 3.3 #8, #5, Conceptual Ch. 4 #2a + new techniques for thinking about #2
- Lecture 16, 5/6/20: Section: 4.2
- Office Hours, 5/7/20: Ch. 4 Conceptual #2d, Webassign 4.1 #4, General Subspace Question, Ch. 3 Conceptual #4
- Lecture 17, 5/8/20: Section: end of 4.2, all of 4.3
- Lecture 18, 5/11/20: Review Day
- 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
- Lecture 19, 5/13/20: Section 4.4
- Office Hours (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
- Lecture 20, 5/18/20: Section 5.1/5.2 (Day 1)
- Office Hours, 5/19/20: Ch. 5 Conceptual #5d, #7
- Lecture 21, 5/20/20: Section 5.1/5.2 (Day 2)
- Office Hours, 5/20/20: Webassign 5.1 #12, Ch. 5 Conceptual #9bde, Midterm 2 #3
- Lecture 22, 5/22/20: Section 6.1
- Midterm 2 Solutions Review: All solutions + alternative solutions
- Office Hours, 5/26/20: Webassign 6.1 #8, #10cd, Ch. 5 Conceptual #2, #8
- Lecture 23, 5/27/20: Sections 6.1, 6.2
- Office Hours, 5/28/20: Ch. 6 Conceptual #4, #5
- Lecture 24, 5/29/20: Section 6.2
- Review Day 1, 6/01/20: Kahoot!, Determinant fact, #3 Lee Aut'18
- Office Hours, 6/02/20: Webassign 6.2 #8, Ch. 6 Conceptual #8, #3be
- Review Day 2, 6/03/20: Kahoot!, #7 Goeckner Aut'18, Commutativity question + Aut '19 Bonus

#### Ebru Bekyel (Section A)

- 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.)
- Midterm 1 Fall 2019
- Midterm 1 Fall 2019 Solutions
- Midterm 1 Winter 2020
- Midterm 1 Winter 2020 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 Fall 2019
- Midterm 2 Fall 2019 Solutions
- Midterm 2 Winter 2020
- Midterm 2 Winter 2020 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 Autumn 2019
- Final Autumn 2019 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

## Course Schedule

- "HW: C1" denotes the first set of conceptual problems, etc.
- "HW: 1.1" denotes the Webassign assignment for section 1.1, etc.
- Lecture: 1.1 denotes a lecture covering section 1.1, etc.

Week | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|

Mar 30 | Lecture: 1.1 | Lecture: 1.1, 1.2 | Lecture: 1.2 | ||

Apr 6 | Lecture: 2.1 | HW: 1.1, 1.2 | Lecture: 2.1 | Lecture: 2.2, HW: C1 | |

Apr 13 | Lecture: 2.3 | HW: 2.1 | Lecture: 2.3 | HW: 2.2, 2.3 | Review, HW: C2 |

Apr 20 | Lecture: 3.1 | Midterm 1 | Lecture 3.1, 3.2 | ||

Apr 27 | Lecture: 3.2 | HW: 3.1 | Lecture: 3.2, 3.3 | HW: 3.2 | Lecture: 3.3, HW: C3 |

May 4 | Lecture: 4.1 | HW: 3.3 | Lecture: 4.2 | HW: 4.1 | Lecture: 4.3, HW: C4 |

May 11 | Review | HW: 4.2, 4.3 | Lecture: 4.4, HW: C5 | Midterm 2 | |

May 18 | Lecture: 5.1/5.2 | HW: 4.4 | Lecture: 5.1/5.2 | HW: 5.1, 5.2 | Lecture: 6.1, HW: C6 |

May 25 | Holiday | Lecture: 6.1, 6.2 | HW: 6.1 | Lecture: 6.2, HW: C7 | |

Jun 1 | Review | HW: 6.2 | Review, HW: C8 | Review | |

Jun 8 | Final Exam |