Math 392 Lecture 24 - Properties and theorems for determinants and the beginning of inverses

Welcome to lecture 24 of Linear Algebra and Vector Calculus!

In this lecture, we finish the chapter on determinants and begin (definition only) the chapter on inverses. That is, we completed chapter 4 in Heuver's Linear Algebra for Calculus and started looking at chapter 5. We cover, with examples, some properties and theorems of determinants that allow us to compute determinants of matrix expressions provided we know the determinants of the matrices in the expressions. We explore how elementary row operations affect matrices and their determinants, and cover a nice application of determinants, Cramer's Rule. We then move on to inverses (of matrices) but didn't get very far. We will pick up next class.

We had some technical difficulties in the beginning, so there's probably a couple of minutes or so of video missing. My apologies. I don't think I said anything in that time that you wouldn't be able to pick up on later, nor do I think I wrote anything on the board that wasn't captured... if you're wondering what everyone was laughing at at the beginning: when we found out the camera was malfunctioning, a student commented, "Oh no, I guess we have to end class!"