Math 231

(Last updated Wednesday, September 28 @2:30pm)

Course Information

  • Instructor: Professor Nicholas Vlamis

  • Instructor Office: 507 Kiely

  • Instructor Email:

  • Office Hour: Monday 2–3pm (or by appointment)

  • Syllabus

  • Textbook: Anton, Howard and Kaul, Anton. Elementary Linear Algebra, twelfth edition. John Wiley & Sons, 2019.

Week 5 (Week of September 26)

  • Quiz 4 will be given in the beginning of class on Wednesday, September 28

Discussed the composition of matrix transformations and used these ideas to prove classical trig identites (e.g. angle-sum identities and double-angle identities). We then introduced the definition of the determinant and went over examples computing the determinant.
  • ***Homework #5 will be posted tomorrow afternoon on account of us having class on Thursday.

  • Solutions to Quiz 4

Week 4 (Week of September 19)

Introduced the notion of diagonal, triangular, and symmetric matrices. Begin our study of matrices as transformations.
  • Note: We have class on Thursday, September 29 (CUNY will follow a Monday schedule that day)

  • Note: Exam 1 is in two weeks on Monday, Oct 3. It will cover Sections 1–9 of Chapter 1.

  • Wednesday's Class Notes

Introduced the notion of a linear transformation from R^n to R^m and showed a one-to-one correspondence between linear transformations and matrix transformations in this setting. We also went over some standard examples of linear transformations from geometry (reflections, projections, rotations), and computed their associated standard matrix.

Week 3 (Week of September 12)

Discussed basic properties of matrix algebra and introduced the inverse of a matrix. Showed how to realize elementary operations as matrix multiplication by elementary matrices, proved a theorem giving several equivalent conditions for a matrix to be invertible, gave an algorithm for finding the inverse of a matrix, and proved that every linear system has 0, 1, or infinitely many solutions.

Week 2 (Week of September 5)

  • No class Monday, September 5 (Labor Day)

  • Quiz 1 will be given in the beginning of class on Wednesday, September 7

  • Syllabus update: your lowest quiz grade will be dropped.

  • Wednesday's Class Notes

Finished discussing using Gauss–Jordan Elmination to solve systems of linear equations, introduced a slate of definitions and operations involving matrices.

Week 1 (Week of August 29)

  • Reading: Read Sections 1.1 and 1.2 in the course textbook. Make sure to read the definition of pivot position, pivot row, and pivot column on page 22.

  • Monday's Class Notes

Introduced a simplified version of Google's PageRank Algorithm, and introduced the notion of a linear system.
  • For those interested, the Google example was lifted from Strogatz's book The Joy of x, which has nice examples of math in the real world.

  • Contact Information Form: Please fill out this form so that I have your preferred email address. I will use the address you provide to send out class announcements.

  • Homework #1 (Associated quiz will be on Wednesday, September 7) ***Updated Wed. Aug. 31 @ 12:30pm

  • Wednesday's Class Notes

Introduced the augmented matrix associated to a linear system, the notion of reduced row echelo form, and learned the Gauss-Jordan Elimination algorithm for finding the reduced row echelon form of a matrix.