Math 2184: Linear Algebra I
Section 10
Fall 2020

Contact Info
Fall 2020

Office: Blackboard
Email: jaydaigle@gwu.edu

Office Hours:

Course Information

Lecture:

Textbook:

Daily Assignments

December 3: Symmetric Matrices and Principal Component Analysis

December 1: Least-squares solutions and linear regression

Slides

November 24: Orthogonal Decomposition

Slides

November 20: Mastery Quiz

November 19: Orthonormal bases

Slides

November 17: Inner Products

Slides

November 12: The Dot Product

Slides

November 10: Diagonalization and Markov Chains

Slides

November 5: Similarity and Trace

Slides

November 3: WeBWorK due, no class

October 29: Change of Basis

Slides

October 27: Complex and Generalized Eigenvectors

Slides

October 22: Determinants and the Characteristic Polynomial

Slides

October 20: No class; midterm due

October 15: Eigenvectors and Eigenvalues

Slides

October 13: Isomorphisms

Slides

October 8: The Matrix of a Linear Transformation

Slides

October 6: Bases and Coordinates

Slides

October 1: Subspaces and Linear Transformations

Slides

September 29: Vector Spaces

Slides

September 24: Bases, Dimension, and Rank

Slides

September 22: Subspaces (and $LU$ factorizations)

Slides

September 17: Matrix Inverses

Slides

September 15: Applications of Linear Functions

Slides

September 14: Webwork due

September 10: Linear Transformations

Slides from Lecture

September 8: Solutions and independence of linear systems

Slides from lecture

September 3: Vectors and Matrix Equations:

Slides from lecture

September 1: Linear Equations and Row Echelon Form

Slides from lecture


Course Goals

This is a standard first course in linear algebra. The main topics are: linear equations; matrix algebra and equations; subspaces and bases; vector spaces; eigenvalues and eigenvectors; determinants; orthogonality and least squares. This corresponds to Chapters 1–7 of Lay, Lay, and McDonald.

By the end of the course, students will acquire the following skills and knowledge:

The course syllabus is available here.

Course notes

Mastery Quizzes

The topics for the quizzes are:

  1. Systems of Linear Equations
  2. Vector Equations and Spans
  3. Linear Independence
  4. Linear Transformations
  5. Matrix Multiplication
  6. Matrix Inverses
  7. Subspaces
  8. Basis and Dimension
  9. Vector Spaces and Subspaces
  10. Vector Space Linear Transformations
  11. Bases and Coordinates
  12. The Matrix of a Linear Transformation
  13. Eigenvectors and Determinants
  14. Characteristic Polynomials and Finding Eigensystems
  15. Complex and Generalized Eigenvectors
  16. Change of Basis
  17. Similarity and Trace
  18. Diagonalization
  19. Dot Product and Projection
  20. Inner Products
  21. Orthogonal Decomposition

Tests

Graphing calculators will not be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.

Textbook

The official textbook for Math 2184 is Linear Algebra and its Applications, Fifth Edition, by Lay, Lay, and McDonald (ISBN-13: 978-0321982384). I will be loosely following this book, and it will be very useful to have, but I will not be assigning problems out of it.

Another perfectly fine book is A First Course in Linear Algebra by Rob Beezer, which is available free online.