Calendar Description: Systems of linear equations; real vectors spaces and subspaces; linear combinations and linear spans; linear dependence and linear independence; applications to systems of linear equations and their solution via Gaussian elimination; bases and dimension of real vector spaces; linear transformations, range, kernel and Rank-Nullity theorem; matrix representation of a linear transformation; composition of linear transformations and matrix multiplication; invertible matrices and determinants; eigenvalues and eigenvectors of square matrices. Applications of the course material to engineering systems are illustrated.
Videos are a mix of lecture capture from Zoom meetings (Winter 2022) and custom-made white-board videos (Winter 2021).
Week 1 – Sets, Functions and Linear Systems
| Notes | Video Playlist | |
| Blank (PDF) Annotated (PDF) | YouTube Panopto | Note: these first videos were lower-resolution as we experimented with how to integrate a tablet with the Zoom stream. Later videos are higher resolution. |
Week 2 – Vector Spaces
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 3 – Subspaces, Linear Combinations
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 4 – Linear Independence and Dependence
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 5 – Solving Linear Systems with RREF
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 6 – Bases and Coordinates for Vector Spaces
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 7 – Dimension; Kernel and Image of Transformations
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 8 – Matrices; Connections with Linear Transformations
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 9 – Linear Transformations and Solving Linear Systems
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 10 – Invertible Matrices and Determinants
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |
Week 11 – More Matrices; Eigenvalue Intro
| Notes | Video Playlist |
| Blank Annotated (PDF) | YouTube Panopto |
Week 12 – Eigenvalues and Eigenvectors
| Notes | Video Playlist |
| Blank (PDF) Annotated (PDF) | YouTube Panopto |