Spring 2021: Linear Algebra II (Math 316)


Instructor Dr. Armin Straub
MSPB 313
(251) 460-7262 (please use e-mail whenever possible)
Office hours MWF, 9-11am, or by appointment

Held virtually using Zoom; please make an appointment by email at least 2 hours in advance.

Class schedule MWF, 8:00-8:55am, in MSPB 410

Due to COVID restrictions, you may only attend those meetings assigned to the cohort you signed up for.

Midterm exams The tentative dates for our two midterm exams are:
Friday, February 26
Monday, April 5
Final exam Monday, May 3 — 8:00-10:00am
Online grades Homework Scores
Exams: USAonline (Canvas)
Syllabus syllabus.pdf

Assignments and course material

In order to be able to view the lecture recordings, you need to be logged into USAonline (Canvas). If you are still running into access issues, then please view the recordings through Panopto Video in our course page on Canvas.

Dates Assignments and course material
#1 01/20
Homework Set 1 (due 2/1)
Lecture notes:
Class schedule:
01/20: online using pre-recorded lectures
01/22: in-person meeting
01/25: online using pre-recorded lectures
#2 01/27
Homework Set 2 (due 2/8)
Lecture notes:
Class schedule:
01/27: in-person meeting
01/29: in-person meeting
02/01: online using pre-recorded lectures
#3 02/03
Homework Set 3 (due 2/15)
Lecture notes:
Class schedule:
02/03: in-person meeting
02/05: in-person meeting
02/08: online using pre-recorded lectures
#4 02/10
Homework Set 4 (due 2/22)
Lecture notes:
Class schedule:
02/10: in-person meeting
02/12: in-person meeting
02/15: online using pre-recorded lectures
#5 02/17
Homework Set 5 (due 2/26)
Lecture notes:
Class schedule:
02/17: in-person meeting
02/19: in-person meeting
02/22: online using pre-recorded lectures
02/24: online via Zoom
zoom-02-24.mp4 (corresponding PDF)
lectures-01-15.pdf (all lecture notes up to now in one big file)
Midterm Exam #1
Format of the exam:
#6 03/01
Homework Set 6 (due 3/14)
Lecture notes:
Lecture recordings:
Class schedule:
03/01: online using pre-recorded lectures
03/03: in-person meeting
03/05: in-person meeting
#7 03/08
Homework Set 7 (due 3/22)
Lecture notes:
Class schedule:
03/08: online using pre-recorded lectures
03/10: student holiday
03/12: in-person meeting
03/15: online using pre-recorded lectures
#8 03/17
Lecture notes:
Lecture recordings:
Class schedule:
03/17: in-person meeting
03/19: in-person meeting
03/22: online using pre-recorded lectures
#9 03/24
Lecture notes:
Lecture recordings:
lecture25-jnf-2.mp4 (corresponding PDF)
lecture25-jnf-3.mp4 (corresponding PDF)
lecture26-de-jnf.mp4 (corresponding PDF)
lecture27-complex.mp4 (corresponding PDF)
Class schedule:
03/24: in-person meeting
03/26: in-person meeting
03/29: online using pre-recorded lectures
03/31: in-person meeting
04/02: online via Zoom
zoom-04-02.mp4 (corresponding PDF)
lectures-16-28.pdf (all lecture notes since the previous exam in one big file)
Midterm Exam #2
#10 04/07
Lecture notes:
Class schedule:
04/07: in-person meeting
04/09: in-person meeting
04/12: online using pre-recorded lectures
#11 04/14
Lecture notes:
Lecture recordings:
Class schedule:
04/14: in-person meeting
04/16: in-person meeting
04/19: online using pre-recorded lectures
#12 04/21
Lecture notes:
Lecture recordings:
Class schedule:
04/21: in-person meeting
04/23: in-person meeting
04/26: online using pre-recorded lectures
04/28: in-person meeting
04/30: online via Zoom
zoom-04-30.mp4 (corresponding PDF)
lectures-29-38.pdf (all lecture notes since the previous exam in one big file)
Final Exam

About the homework

  • Homework problems are posted for each unit. Homework is submitted online, and you have an unlimited number of attempts. Only the best score is used for your grade.

    Most problems have a random component (which allows you to continue practicing throughout the semester without putting your scores at risk).

  • Aim to complete the problems well before the posted due date.

    A 15% penalty applies if homework is submitted late.

  • Collect a bonus point for each mathematical typo you find in the lecture notes (that is not yet fixed online), or by reporting mistakes in the homework system. Each bonus point is worth 1% towards a midterm exam.

    The homework system is written by myself in the hope that you find it beneficial. Please help make it as useful as possible by letting me know about any issues!


As part of this course, we will explore the open-source free computer algebra system Sage to assist with more involved calculations.

If you just want to run a handful quick computations (without saving your work), you can use the text box below.

A convenient way to use Sage more seriously is This free cloud service does not require you to install anything, and you can access your files and computations from any computer as long as you have internet. To do computations, once you are logged in and inside a project, you will need to create a "Sage notebook" as a new file.

Here are some other things to try:

  • Sage makes solving least squares problems pleasant. For instance, to solve Example 45 in Lecture 8:
    A = matrix([[1,2],[1,5],[1,7],[1,8]]); b = vector([1,2,3,3])
  • Sage can compute QR decompositions. For instance, we can have it do Example 70 in Lecture 13 for us:
    A = matrix(QQbar, [[0,2,1],[3,1,1],[0,0,1],[0,0,1]])
    The result is a tuple of the two matrices Q and R. If that is too much at once, A.QR(full=false)[0] will produce Q, and A.QR(full=false)[1] will produce R. (Can you figure out what happens if you omit the full=false? Check out the comment under "Variations" for the QR decomposition in the lecture sketch. On the other hand, the QQbar is telling Sage to compute with algebraic numbers (instead of just rational numbers); if omitted, it would complain that square roots are not available.)