Rutgers University Fall 2022
Math 350 — Linear Algebra
Section 1
Lectures: TF 10:20-11:40am in SEC-203
Office hours: Tuesdays 3:20 - 4:00pm and Fridays 2:00 - 2:40pm in Hill 440 and by appointment.
Welcome to Math 350! I will continually add to this page as the course progresses.
Tentative Schedule
| Week | Lecture dates | Sections | Topics/Notes |
|---|---|---|---|
| 1 | 9/6, 9/9 | Sections 1.1-1.4 | Introduction, abstract vector spaces, subspaces, span |
| 2 | 9/13, 9/16 | Sections 1.5-1.6 | Linear independence, bases. Skip Lagrange interpolation for now. |
| 3 | 9/20, 9/23 | Sections 2.1-2.2 | Linear transformations, matrix representations |
| 4 | 9/27, 9/30 | Sections 2.3-2.4 | Composition, invertibility |
| 5 | 10/4, 10/7 | Ch. 1-2 | Review and Exam 1 (in class) |
| 6 | 10/11, 10/14 | Section 2.5 and Ch. 3 | Change of basis. Note: the material in Ch. 3 was covered in the prerequisite Math 250. |
| 7 | 10/18, 10/21 | Sections 4.1-4.4 | Determinants and their properties |
| 8 | 10/25, 10/28 | Sections 5.1-5.2 | Eigenvalues, eigenvectors, diagonalizability |
| 9 | 11/1, 11/4 | Section 5.4 | Invariant subspaces, the Cayley-Hamilton theorem |
| 10 | 11/8, 11/11 | Sections 7.1, 7.2 | Jordan canonical form |
| 11 | 11/15, 11/18 | Sec 2.5, Ch. 3-5, 7 | Review and Exam 2 (in class) |
| 12 | 11/23* | Chapter 6 | Inner product spaces |
| 13 | 11/29, 12/2 | Chapter 6 | Normal and self-adjoint operators |
| 14 | 12/6, 12/9 | Chapter 6 | Unitary and orthogonal operators |
| 15 | 12/13 | All | Review |
| 16 | 12/16 | All | Final Exam 8:00-11:00am |
Homeworks and Quizzes
HW #9, Due Wednesday, 12/7 at 11:59pm.
[Problems] [Solutions]Quiz #9, in class on 11/29
[Quiz 9 Solutions]Quiz #8, in class on 11/8
[Quiz 8 Solutions]HW #8, Due Saturday, 11/12 (at 11:59pm)
[Problems] [Solutions]Quiz #7, in class on Friday 11/4
[Quiz 7 Solutions]HW #7, Due Saturday, 11/5 (at 11:59pm)
[Problems] [Solutions]Quiz #6, in class on 10/25.
[Quiz 6 Solutions]HW #6, Due Friday, 10/28 (at midnight)
[Problems] [Solutions]Quiz #5, in class on 10/18.
[Quiz 5 Solutions]HW #5, Due Friday, 10/21.
[Problems] [Solutions]Quiz #4, in class on 10/11.
The problems were 1b and 4c from the exam. See [Exam solutions].HW #4, Due Monday, 10/17
[Problems] [Solutions]Quiz #3, in class on 9/27.
[Quiz 3 Solutions]HW #3, Due 9/30
[Problems] [HW3 Solutions]Quiz #2, in class on 9/20.
[Quiz 2 Solutions]HW #2, Due 9/23:
Section 1.3, Problems 23(a), 23(b), 30, 31(a), 31(b), 31(c), 31(d).
Section 1.5, Problems 2(c), 8, 10, 18
Section 1.6, Problems 11, 32(a), 32(b), 32(c)
Each problem is worth 2 points, 30 points total.
[HW2 Solutions]Quiz #1, in class on 9/13.
[Quiz 1 Solutions]HW #1, Due 9/16:
Section 1.2, Problems 2, 4(a), 4(f), 8, 9, 12, 17
Section 1.3, Problems 5, 8(a), 8(b)
Section 1.4, Problems 1(a), 1(c), 1(f), 4(a), 5(g)
Each problem is worth 2 points, 30 points total.
Notes: In Sec 1.2 #8 and #9: Explicitly quote each vector space axiom (among (VS 1)--(VS 8)) that you use in each step. In #8, explain why parentheses are not needed in the right-hand side of the formula. In #12, you need to show that all the parts of the definition of vector space hold.
[HW1 Solutions]
Useful links:
Syllabus
Math 250 Review Notes
3Blue1Brown (Lots of animation, great for visualizing)
Khan academy (Perfect for pretending we’re back in lockdown)
math.stackexchange.com (Q&A forum for conceptual questions, don’t ask for homework solutions)
Exam 1 Materials:
Exam 1 Review Notes
Sample Exam1 [Solutions]
Review office hours recording Passcode: Ha4bg%%R
Exam 1 Problems [Solutions] (Bonus exam point if anyone finds a mathematical error in the solutions)
Exam 2 Materials:
Exam 1+2 Review Notes
Sample Exam 2 [Solutions] (For 5b, you should be table to solve it if given the definition of “cycle of generalized eigenvectors”. No question like 5c will appear on our exam)
Review office hours recording (Passcode: u@f37s.5)
Exam 2 Problems [Solutions] (Bonus exam point if anyone finds a mathematical error in the solutions)
Final Exam Materials:
Exam 1+2+Final Review Notes (including practice problems! Will be updated as we approach the final)
[Sample Final Exam] [Solutions]
Final Exam Solutions
Announcements:
12/14 — Will hold special zoom office hours on Wednesday 12/14, from 5:30-7pm. [Zoom link]
12/13 — Today’s lecture was online. [Lecture Notes] [Zoom recording of lecture] Recording password: “CDg$^c1P”
12/12 — The lecture on Tuesday 12/13 will be ONLINE. [Zoom link]
12/11 — Homework 9 solutions are up. Final Review Notes have been updated. SIRS available [here]
12/9 — Today’s office hours will be via Zoom, at the usual time (2:00 - 2:40pm). [Zoom invite link]
12/9 — Today’s lecture was online. [Lecture notes] [Zoom recording of lecture] Recording password: “=^SMD1?k”
12/8 — The lecture on Friday 12/9 will be ONLINE. [Zoom link]
12/2 — Homework 9 had an error in the formulation of additional problem 1. It has now been fixed, and the deadline has been extended.
11/29 — Somehow I accidentally deleted all the previous announcements. Anyway, homework 9 is up. Quiz solutions will be uploaded later tonight.