These linear algebra resources were created while I was TAing MATH 1850U at Ontario Tech University in the Fall 2023 term. They should still be applicable to other courses at Ontario Tech University, notably MATH 2050U, as well as to other students outside of Ontario Tech University who are studying a first course in linear algebra. These materials follow Elementary Linear Algebra by Howard Anton, 11e. For the more proof-based sections of the course, I may use Linear Algebra Done Wrong by Sergei Treil. Topics will be presented in the order of Anton. Those not using Anton or Treil will still find these resources helpful.
Jump to Lecturette Recordings
Jump to Lecturette Notes
Video Examples
- Introduction to matrices and linear systems
- Gaussian elimination
- Matrix operations
- Matrix inverses
- Vandermonde interpolation
- Determinants
- Cramer's rule
- Introduction to vectors
- Norms and dot products
- ISBNs
- Orthogonal vectors
- Vectors and geometry
-
Vector space axioms
Note: For more videos on this topic, see the videos listed as 1.X in Advanced Linear Algebra -
Subspaces
Note: For more videos on this topic, see the videos listed as 1.X in Advanced Linear Algebra - Linear independence
- Wronskian
- Span
- Basis
Lecturette Recordings
Note: The quality of the recordings may not be ideal. They are not meant to replace in-class attendance. They should primarily serve as a supplemental aid to students.- Linear Systems and Gaussian Elimination
- Working with Matrices
- Inverses and Determinants
- Determinants and Cramer's Rule
- Vector Spaces and Subspaces
- Linear Independence and Span
- Basis and Dimension
- Linear Transformations
- Eigenpairs
- Diagonalization
Below, you will find midterm review recordings.
Problem Sets
Note: These problem sets were used during a summer course, and as such are more condensed. They combine multiple topics together in each set.- Basics of Linear Systems
- Inverses and Determinants
- Euclidean Vectors and Vector Spaces
- Basis and Fundamental Spaces
- Linear Transformations and Eigenpairs
Challenge Questions
Lecturette Notes
Note: The notes provided here are handwritten and scanned. The scans aren't perfect, but I hope are enough for students of mine to refer back to.- Linear Systems and Gaussian Elimination
- Working with Matrices
- Inverses and Determinants
- Determinants and Cramer's Rule
- Vector Spaces and Subspaces
- Linear Independence and Span
- Basis and Dimension
- Fundamental Spaces and Rank-Nullity Theorem
- Linear Transformations
- Eigenpairs
- Diagonalization
- Inner Products and Gram-Schmidt Process
For those who want to go a step further or prefer learning by diagrams, here is a fantastic resource you can use by Prof. Pawel Sobocinski.