MAT 2580 Linear Algebra

Professor Poirier | D712 | Spring 2026

Week 15 checklist

Tuesday, May 12 to Monday, May 18

Lessons

  • 5.9. The Coordinates of a Vector Relative to a Basis (Change of Coordinates)
    • I haven’t watched all of the videos in this playlist, but this account tends to be reliable; just watch out if they use notation that is different from the notation we are using
  • 5.10 The Matrix of a Linear Transformation II
  • 7.1 Eigenvalues and Eigenvectors of a Matrix

WeBWorK

Note: All old WeBWorK sets will be reopened and due Friday night, May 22 (hard deadline). The newer sets are due at 11:59pm and the older sets are due one minute later at 12:00am

For this week’s topics:

  • Linear Transformations Relative to Basis
  • Eigenvectors and Eigenvalues

OpenLab

Note: You may complete/update any old OpenLab assignment before Friday, May 22 at 11:59pm for participation credit. Make sure that you follow the directions about title and category for posts. You can see old assignment instructions in the old weekly checklists

  • [Group assignment #1] Test #3 solutions
    • Official deadline: Monday, May 18
    • Same instructions as for Test #1 solutions
    • Title: Test #3 Solutions – Group n (where n is your group number)
    • Categories:
      • Group n (where n is your group number)
      • Test #3 Solutions
    • Test #3 Version B
  • [Group assignment #2] Practice final exam (instructions)

Other

  • Office hours on Tuesday, May 11 (N618) will end at 12:30
  • Student evaluation of teaching: fill these out in Brightspace for all of your classes by May 15
    • See student instructions here
    • Bonus: read an article about bias in student evaluations of teaching like this one
    • Bonus: If you really enjoyed any of your classes this semester, you can also send your professor an email telling them exactly what you liked about their class.
  • Final exam is Tuesday, May 26 in class
    • Absences are excused only in extraordinary circumstances (college procedure and paperwork must be followed)
    • Plan to arrive early; latecomers will not be given extra time
  • WU grade:
    • This grade is for an “unofficial withdrawal” and is for students who stop attending class before final exam week. The WU grade will not have punitive impact on student’s GPA, but can impact a student’s full-time status, which can impact financial aid and international-student-visa status.
    • Students who attend class after May 16 will not be eligble for a WU.

Matrix of linear transformations Exercise

2.6E24
Say we had R^2 -> R^3 -> R^4 from two linear transformations, S * T is linear because its valid under addition and scalar multiplication for all R^n.
Say we had <1, 2> -> <1,2,3> -> <2,4,6, 6> from
[1 0 and [2 0 0

0 1 0 2 0

1 1] 0 0 2

1 1 1]

as our transformation A vectors, it moves from R^2 to R^3 to R^4 and we can put any scale of this input in, and it’ll scale the output proportionally. <2,4> -> <2,4,6>

-> <4, 8, 12, 12>
Also we can add any two scales of input vectors and still get the same output summed. <3,6> from <1,2> + <2,4> -> <3,6,9> -> <6, 12, 18, 18>

Group assignment – practice final exam

Due Monday, May 18

Your final exam will have the same structure as your three term tests. One of the five calculation questions will cover diagonalization. This question will have multiple parts and may be worth 15 points instead of the usual 10.

As a group, create your own practice final exam (just the questions, no answers or solutions yet). You may use previous test questions, WeBWorK problems, or textbook homework problems. (You may leave off the diagonalization problem for now and add it later if you wish.)

  • Title: Practice final exam – Group n (where n is your group number)
  • Categories
    • Group n (where n is your group number)
    • Practice final exam
  • Include names/initials of group members who participated
« Older posts