Matrix Algebra

Fall 2022



Instructor: Matt Kerr
Office: Cupples I, Room 114
e-mail: matkerr [at] wustl.edu
Office Hours: Monday 8-9 PM (on Zoom), Wednesday 3-3:50 PM and Friday 4-5 PM.
Note: for now, please wear a mask if you attend the in-person office hours.

Prerequisites:

Math 132 (Calculus II)

Class Schedule:

[Please note: Math 309 has 4 sections this semester. This webpage only pertains to section 1.]

Lectures are on Monday, Wednesday, and Friday from 11-12 in Hillman 70, beginning Monday Aug. 29 and ending with a final exam review class on Friday December 9. There are class holidays on Sept. 5 (Labor Day), Oct. 10-11 (Fall break), and Nov. 23-25 (Thanksgiving).

Midterm Exam 1: Oct. 7 (in class), on Chapters 1--3
Midterm Exam 2: Nov. 14 (in class), thru Section 5.7
Final Exam: 10:30-12:30, Dec. 20, in Hillman 70

Regarding missed exams, see the Grading Policy section below. Calculators aren't allowed, but the exams will not be computationally heavy.

Copies of old exams are maintained at this link. Exam solutions will appear on Canvas.

Textbook:

David Lay, Steven Lay, and Judi McDonald, Linear Algebra and its Applications (5th Ed.), Pearson, 2016.

We will cover Chapters 1-6 and the beginning of 7. The publisher maintains an online student resource page which includes review sheets and practice exams. Last but not least, the original author of the previous editions (David Lay) has some friendly advice on learning from his book.

Course Syllabus:

This is an introductory course in linear/matrix algebra. You can expect a mild amount of abstraction, but the emphasis is on topics which are useful in science, engineering, and business. My goal is for each of you to come away in 15 weeks with a good understanding of:

  • Linear systems, row-reduction, and matrix equations
  • Linear transformations, invertibility, rank+nullity
  • Determinants
  • Vector spaces, basis and dimension
  • Eigenvectors and eigenvalues, diagonalization
  • Inner products, orthogonality, Gram-Schmidt
  • The spectral theorem and quadratic forms


  • Assignments:

    These will comprise:

  • A weekly Webwork due on Friday (at 8 PM) --- about 5-10 computational problems, covering up through Wednesday's lecture. Webwork must be accessed through Canvas. The webwork due on Friday will become available on Tuesday morning.

  • A weekly written homework due by 5 PM on Tuesday (except for HW 1, due Wednesday) --- around 10 problems, more theoretical in nature and covering the previous week's lectures. (The problems are listed below the next table.) You will submit these as a PDF upload through Gradescope (or through Canvas, if this link doesn't work). Solutions will appear on Canvas.

  • I encourage you to visit my office hours (chosen with this schedule in mind) to discuss both kinds of problem sets, and to form study groups to discuss the more difficult problems (though solutions must be written up independently). Regarding late homework, cf. the Grading Policy below.

    Week of ... Homework (due Tues) Webwork (due Fri)
    Aug. 29 (Week 1) no WW no HW
    Sep. 5 (Week 2) HW 1 (due Wed.) WW 1
    Sep. 12 (Week 3) HW 2 WW 2
    Sep. 19 (Week 4) HW 3 WW 3
    Sep. 26 (Week 5) HW 4 WW 4
    Oct. 3 (Week 6) HW 5 no WW
    Oct. 10 (Week 7) no HW WW 5
    Oct. 17 (Week 8) HW 6 WW 6
    Oct. 24 (Week 9) HW 7 WW 7
    Oct. 31 (Week 10) HW 8 WW 8
    Nov. 7 (Week 11) HW 9 WW 9
    Nov. 14 (Week 12) no HW WW 10
    Nov. 21 (Week 13) HW 10 no WW
    Nov. 28 (Week 14) HW 11 no WW
    Dec. 5 (Week 15) HW 12 no WW

    HW #1 (due Sept. 7): §1.1: #24, 27, 33, 34; §1.2: #4, 12, 16, 30; §1.3: #14, 18, 22, 32
    HW #2 (due Sept. 13): §1.4: #10, 16, 18, 24; §1.5: #6, 12, 16, 30; §1.6: #8, 14
    HW #3 (due Sept. 20): §1.7: #26, 36, 38; §1.8: #18, 30, 34; §1.9: #8, 18, 26, 30
    HW #4 (due Sept. 27): §2.1: #12, 22, 24, 26; §2.2: #16, 24, 32; §2.3: #6, 14; §2.4: #6; §2.5: #2, 8
    HW #5 (due Oct. 4): §2.3: #20, 38; §2.6: #4; §3.1: #10, 18; §3.2: #10, 26, 30, 36; §3.3: #32
    HW #6 (due Oct. 18): §4.1: #6, 16, 32; §4.2: #6, 10, 22, 32; §4.3: #8, 14; §4.4: #10
    HW #7 (due Oct. 25): §4.4: #12, 14, 32; §4.5: #4, 14, 22; §4.6: #10, 22, 30; §4.7: #8
    HW #8 (due Nov. 1): §4.8: #14, 30; §4.9: #4, 14, 18; §5.1: #16, 36; §5.2: #8, 14, 18
    HW #9 (due Nov. 8): §5.3: #6, 14, 16, 26; §5.4: #12, 14, 26; §5.5: #4, 8, 14
    HW #10 (due Nov. 22): §5.6: #2, 4; §5.7: #4; §6.1: #14, 26, 28; §6.2: #12, 14, 16, 34
    HW #11 (due Nov. 30): §6.3: #12, 16, 24; §6.4: #6, 14, 20; §6.5: #2, 6, 10, 16
    HW #12 (due Dec. 8 at 11pm): §6.6: #2, 6; §6.7: #26; §7.1: #10, 20, 32; §7.2: #8, 10, 12, 20

    Graders: Raina Foreman (raina.foreman [at] wustl.edu); Ian Marroquin (ianmarroquin [at] wustl.edu)

    Lecture Notes:

    In the calendar below I will post my notes for each lecture, after the class takes place. Click on the "Lec X" link (once it is active) for the notes. The sections covered in the lecture are also displayed in the table (though these sections may not be covered in full). The "week of" date refers to Monday.

    The lecture notes are intended to help you prepare for exams, fill in bits you may have missed in lecture, or even avoid taking notes altogether. They are not intended, however, as a substitute for class attendance and reading the book.

    Week Monday Wednesday Friday
    1 [Lec 1] 1.1 [Lec 2] 1.2 [Lec 3] 1.3
    2 Labor Day [Lec 4] 1.4,6 [Lec 5] 1.5
    3 [Lec 6] 1.7 [Lec 7] 1.8 [Lec 8] 1.9
    4 [Lec 9] 2.1 [Lec 10] 2.2,3 [Lec 11] 2.3,4,5
    5 [Lec 12] 2.6,3.1 [Lec 13] 3.2 [Lec 14] 3.3
    6 [Lec 15] 4.1 [Lec 16] 4.2 [Exam 1]
    7 Fall Break [Lec 17] 4.3 [Lec 18] 4.4
    8 [Lec 19] 4.5 [Lec 20] 4.6 [Lec 21] 4.7
    9 [Lec 22] 4.8,9 [Lec 23] 5.1,2 [Lec 24] 5.2,3
    10 [Lec 25] 5.3,4 [Lec 26] 5.4 [Lec 27] 5.5
    11 [Lec 28] 5.6 [Lec 29] 5.7 [Lec 30] 6.1
    12 [Exam 2] [Lec 31] 6.2 [Lec 32] 6.3,4
    13 [Lec 33] 6.4,5,6 Thanksgiving Break
    14 [Lec 34] 6.5,6 [Lec 35] 6.7 [Lec 36] 7.1
    15 [Lec 37] 7.2 [Lec 38] 7.4 [Lec 39] Review


    Grading Policy:

    Homework is worth 30%, Webwork 10%, Midterm Exam 1 and Midterm Exam 2 are worth 15% each, and the Final Exam is worth 30%. I will drop your lowest 2 homework and lowest 2 webwork scores.

    Curving and grade scale: In the event that the average score on any exam is less than 75%, all exam scores will be adjusted upward by adding a constant to everyone's score (so that the average is 75%). No adjustment is made if the average is above 75%. The grade scale is as follows:

    A+ A A- B+ B B- C+ C C- D F
    TBA 90+ [85,90) [80,85) [75,80) [70,75) [65,70) [60,65) [55,60) [50,55) [0,50)

    The Pass/Fail policy is that you must get at least a C- to earn a "Pass".

    Grades will be kept track of on Canvas, though Webwork will only be entered there as block scores at the end of the course. (In the meantime, you will be able to keep track of your scores on individual WW sets on the website where you hand them in.)

    If you have to miss a midterm exam for a legitimate reason, you will be given an excused absence for that exam, and your grade will be calculated from the homework and other taken exams. Of course verified illness and serious family emergency are legitimate reasons. Regarding other conflicts, e-mail me as soon as you know about them.

    Verified illness and serious family emergency are in general the only acceptable reasons for missing the final exam. In this event, you will receive an Incomplete and will have to make up the exam later to resolve this.

    To have any excused absence approved, please contact Blake Thornton (bthornton [at] wustl.edu) and cc me in the e-mail.

    In general, credit will be given for late Webwork/Homework only in the event of illness or emergency.

    This link takes you to the standard university policies on academic integrity.

    Academic Support:

    Lidya Wolde (l.f.wolde [at] wustl.edu) is the drop-in mentor for Matrix Algebra this Fall. Her mentoring hours are 5-7 Mondays in Simon 017. Drop in for questions about HW or WW, or to work on problems with classmates.