Matthew L. Wright
Associate Professor, St. Olaf College

Linear Algebra

MATH 220 ⋅ Spring 2025

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Friday
February 7
Course introduction; linear equations
Do the following before next class:
Monday
February 10
Lines and linear equations (textbook section 1.1)

MSCS Colloquium: Paul Zorn, "Digging for Roots of Unity," Monday, February 10, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Re-read Section 1.1 in the text. Think carefully about the definitions, properties, and examples, which should make more sense after today's class.
  • Complete Written Homework 1, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
  • Start Mathematica Lab 1, which is due Friday. Before Wednesday, work through the lab notebook, practice creating code cells and text cells, and identify any questions that you have.
  • Read Section 1.2 in our text, at least through Example 4, and complete the Preview Exercises. Submit your responses to the Section 1.2 Preview Exercises assignment on Moodle before class on Wednesday.
Wednesday
February 12
Linear systems (textbook section 1.2)

Bonus video: Paths to Math: John Urschel

Do the following before next class:
  • Re-read Section 1.2 in the text, continuing through the end of the section. Also skim through the examples in Section 1.3. Complete the Preview Exercises. Submit your responses to the Section 1.2-1.3 Preview Exercises assignment on Moodle before class on Friday.
  • Complete Written Homework 2, which is due Friday at 9:30pm. Try to complete this before class on Friday, though there is time to ask last-minute questions Friday afternoon.
  • Finish Mathematica Lab 1. Prepare your solutions in a new Mathematica notebook, and submit your notebook to the Mathematica Lab 1 assignment on Moodle.
Friday
February 14
Linear systems and matrices (textbook section 1.2)

Science and Math Research and Internship Fair: Friday, February 14, 3:30–4:30pm, Regents 356

Do the following before next class:
  • Read Section 2.1 in the text and complete the Preview Exercises. Submit your responses to the Section 2.1 Preview Exercises assignment on Moodle.
  • Complete Written Homework 3, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
  • Begin Mathematica Lab 2, which is due Wednesday. Work through the lab notebook and practice using matrices in Mathematica. Start working on the problems (put your solutions in a new notebook).
Monday
February 17
Vectors (textbook section 2.1)

MSCS Colloquium: A CURIous Invitation, Monday, February 17, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Read Section 2.2 of our text, at least through Example 3, and complete the Preview Exercises. Submit your responses to the Section 2.2 Preview Exercises assignment on Moodle.
  • Complete Written Homework 4, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
  • Finish Mathematica Lab 2, which is due Wednesday. Prepare your solutions in a new Mathematica notebook, and submit your notebook to the Mathematica Lab 2 assignment on Moodle.
Wednesday
February 19
Linear combinations and span (textbook section 2.2)

Bonus video: Eugenia Cheng on The Late Show

Do the following before next class:
  • Re-read Section 2.2 in the text (read the whole section). There are no preview exercises due Friday.
  • Complete Written Homework 5, which is due Friday at 9:30pm. Try to complete this before class on Friday, though there is time to ask last-minute questions Friday afternoon.
  • Begin Mathematica Lab 3, which is due Monday. For this lab, you will need to download and save image1.png, image2.png, image3.png, and image4.png to your computer. Work through the lab notebook and practice using matrices in Mathematica. Start working on the problems (put your solutions in a new notebook).
Friday
February 21
Span and linear independence (textbook sections 2.2 and 2.3)
Do the following before next class:
Monday
February 24
Linear independence (textbook section 2.3)

Statistics and Economics lecture: Prof. Carola Binder, "Inflation in American Democracy," Monday, February 24, 7:00–8:00pm in Tomson 280

Do the following before next class:
  • Complete Written Homework 7, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
  • Begin Mathematica Lab 4. While this lab is not due until due next Monday (March 3), you should complete it this week as part of your studying for the exam.
  • Read the Exam 1 Guidance and study for the exam. Note that solutions to all past assignments are posted on Moodle.
Wednesday
February 26
Review day

Bonus: Federico Ardila on Math, Music and the Space of Possibilities

Do the following before next class:
  • Work on Mathematica Lab 4. While this lab is not due until due Monday, it is recommended that you complete it this week as part of your studying for the exam.
  • Read the Exam 1 Guidance and study for the exam. The textbook has a lot of good practice problems in each section and also the supplementary exercises at the end of Chapters 1 and 2. Note that solutions to all past assignments are posted on Moodle.
Friday
February 28
Do the following before next class:
Monday
March 3
Linear transformations (textbook section 3.1)

MSCS Colloquium: What can I do with my computer science degree? Monday, March 3, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Correct any exam problems you missed. Follow instructions distributed in class. Corrections are due at the beginning of class on Wednesday.
  • Read Section 3.1 of our text, from Theorem 3.3 through the end of the section, and complete the Preview Exercises. Submit your responses to the Section 3.1 Part 2 Preview Exercises assignment on Moodle.
  • Complete Written Homework 8, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
Wednesday
March 5
Linear transformations (textbook section 3.1)

Bonus: Why is Mathematics Useful — Robert Ghrist, and Calculus GREEN

Do the following before next class:
Friday
March 7
Matrix algebra (textbook section 3.2)
Do the following before next class:
  • Finish reading Section 3.2 in our textbook. There are no preview exercises for Monday.
  • Watch Matrix multiplication as composition by 3Blue1Brown.
  • Complete Written Homework 10, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
  • Finish Mathematica Lab 5, which is due Monday. Prepare your solutions in a new Mathematica notebook, and submit your notebook to the Mathematica Lab 5 assignment on Moodle.
Monday
March 10
Matrix algebra (textbook section 3.2)
Do the following before next class:
Wednesday
March 12
Matrix inverses (textbook section 3.3)

Pamela Harris: MEET a Mathematician! Pamela E. Harris

Women in STEM Alumni Career Panel Wednesday, March 12, 7:00pm, Tomson 280

Do the following before next class:
  • Read Section 3.5 of our text through Example 3 and complete the Preview Exercises. Submit your responses to the Section 3.5 Preview Exercises assignment on Moodle.
  • Complete Written Homework 12, which is due Friday at 9:30pm. Try to complete this before class on Friday, though there is time to ask last-minute questions Friday afternoon.
  • Finish Mathematica Lab 6, which is due Friday. Prepare your solutions in a new Mathematica notebook, and submit your notebook to the Mathematica Lab 6 assignment on Moodle.
Friday
March 14
Markov chains (textbook section 3.5)

MSCS Lecture: Dr. Pamela Harris — How to choose your own mathematical adventures Friday, March 14, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Read Section 4.1 of our text through Definition 4.4 and complete the Preview Exercises. Submit your responses to the Section 4.1 Preview Exercises assignment on Moodle.
  • Complete Written Homework 13, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
Monday
March 17
Subspaces (textbook section 4.1)
Do the following before next class:
  • Finish reading Section 4.1 of our text and complete the Preview Exercises. Submit your responses to the Section 4.1 Part 2 Preview Exercises assignment on Moodle.
  • Complete Written Homework 14, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
  • Begin Mathematica Lab 7, which is due Friday Monday. This lab should not be long or difficult, but it's still important to start early and ask questions if you run into trouble.
Wednesday
March 19
Subspaces and nullspaces (textbook section 4.1)

Bonus videos: Satyan Devadoss — Blue Collar Mathematics and Mage Merlin's Unsolved Mathematical Mysteries

Do the following before next class:
Friday
March 21
Basis and dimension (textbook section 4.2)

BRIDGES: Common Ground Friday, March 21, 3:30–5:00pm, RNS 356

Do the following before next class:
  • Read the rest of Section 4.2 in the textbook. There are no preview exercises for Monday.
  • Watch Three-dimensional Linear Transformations by 3Blue1Brown. This video will help you think geometrically about linear transformations in 3D.
  • Complete Written Homework 16, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
  • Finish Mathematica Lab 7, which is due Monday. Prepare your solutions in a new Mathematica notebook, and submit your notebook to the Mathematica Lab 7 assignment on Moodle.
  • Read the Exam 2 Guidance and start studying for the exam.
Monday
March 24
Basis and dimension (textbook section 4.2)

MSCS Colloquium: Michael Culshaw-Maurer, Lessons from a reluctant data scientist, Monday, March 24, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Complete Written Homework 17, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
  • Study for the exam: re-read the Exam 2 Guidance, review theory, work on practice problems, come to office hours and help sessions.
Wednesday
March 26

Bonus videos: Christmas Lectures 2019: How to Get Lucky — Hannah Fry and The Future with Hannah Fry

Do the following before next class:
  • Study for the exam: re-read the Exam 2 Guidance, review theory, work on practice problems, come to office hours and help sessions.
  • Prepare your index card of notes (4 inch by 6 inch, 1 side) for the exam.
Friday
March 28
Do the following before next class:
Have a great spring break! No class March 31–April 4.
Monday
April 7
Row and column spaces (textbook section 4.3)

MSCS Colloquium: Mike Dabkowski, Non-compactness of the product of a composition operator and an adjoint of such and operator, Monday, April 7, 3:30–4:30pm in RNS 210

Do the following before next class:
  • Correct any exam problems you missed. Follow instructions distributed in class. Corrections are due at the beginning of class on Wednesday.
  • Read Section 5.1 of our text, at least through Example 5, and complete the Preview Exercises. Submit your responses to the Section 5.1 Preview Exercises assignment on Moodle.
  • Optionally, begin Written Homework 18, which is due Friday.
Wednesday
April 9
The determinant (textbook section 5.1)
Do the following before next class:
  • Re-read Section 5.1, then skim Section 5.2 of our text. There are no Preview Exercises for Friday.
  • Finish Written Homework 18, which is due Friday at 9:30pm. Try to complete this before class on Friday, though there is time to ask last-minute questions Friday afternoon.
  • Begin Mathematica Lab 8, due Wednesday, April 16.
Friday
April 11
The determinant (textbook section 5.2)
Do the following before next class:
  • Read the subsection Areas and Determinants in Section 5.3, pages 237–241. This explains the general idea behind problems 6–8 from the worksheet today.
  • Read Section 6.1 of our text, at least through Example 6, and complete the Preview Exercises. Submit your responses to the Section 6.1 Preview Exercises assignment on Moodle.
  • Finish Written Homework 19, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
  • Work on Mathematica Lab 8, which is due Wednesday, April 16. Try to finish this by Monday, so that you have time to ask questions in case you get stuck.
Monday
April 14
Eigenvalues and eigenvectors (textbook section 6.1)
Do the following before next class:
  • Re-read Section 6.1 of our text. There are no preview exercises for Wednesday.
  • Finish Mathematica Lab 8. which is due Wednesday at 9:30pm. Submit your lab notebook to the Mathematica Lab 8 assignment on Moodle.
  • Finish Written Homework 20, which is due Wednesday at 9:30pm. Try to complete this before class on Wednesday, though there is time to ask last-minute questions Wednesday afternoon.
Wednesday
April 16
Eigenvalues and eigenvectors (textbook section 6.1)

Bonus: video How Not to Be Wrong: The Power of Mathematical Thinking - with Jordan Ellenberg and article The Psychology of Statistics by Jordan Ellenberg

MSCS Recital: Wednesday, April 16, 7pm, Ytterboe Lounge

Do the following before next class:
  • Re-read Section 6.1 of our text. There are no preview exercises for Friday.
  • Complete Written Homework 21, which is due Friday at 9:30pm. Try to complete this before class on Friday, though there is time to ask last-minute questions Friday afternoon.
Friday
April 18
Eigenvalues and matrix powers (textbook sections 6.1 and 6.2)
Do the following before next class:
  • Watch Eigenvectors and Eigenvalues by 3Blue1Brown. You may stop after 13 minutes, since after that he talks about change of basis, which we have not studied.
  • Read Section 6.2 of our text and complete the Preview Exercises. Submit your responses to the Section 6.2 Preview Exercises assignment on Moodle.
  • Complete Written Homework 22, which is due Monday at 9:30pm. Try to complete this before class on Monday, though there is time to ask last-minute questions Monday afternoon.
Monday
April 21
Diagonalization (textbook section 6.2)
Wednesday
April 23
Dot products and orthogonality (textbook section 8.1)
Do the following before next class:
  • To be announced
Friday
April 25
Projections (textbook section 8.2)
Do the following before next class:
  • To be announced
Monday
April 28
Least squares regression (textbook section 8.5)
Do the following before next class:
  • To be announced
Wednesday
April 30
Review
Do the following before next class:
Friday
May 2
Exam 3
Do the following before next class:
Monday
May 5
Vector spaces (textbook section 7.1)
Do the following before next class:
Wednesday
May 7
Span and independence (textbook section 7.2)
Do the following before next class:
  • To be announced
Friday
May 9
Basis and dimension (textbook section 7.3)
Do the following before next class:
  • To be announced
Monday
May 12
Review
We've reached the end of the semester! A few last things to do:
  • To be announced
Saturday
May 17
Final Exam 1:00–3:00pm