Linear Algebra 8a: Linear Systems Terminology

[darrenpeck]

Every qualified teacher should learn the introduction that understanding where the solutions come from and what they look is vital. Why is it so rare to find a professor who lectures with this conviction. I sincerely hope other professors will learn from such an introduction. Thank you for the awesome teaching and pedagogy and subject knowledge!

[Rangerpl]

Teaching the fundamental concepts of vector spaces first, and introducing linear systems, matrices and Gaussian elimination later is a great approach. In my LA class, we learned about Gaussian elimination the first week and I think this robbed us of some intuition by giving us a sledgehammer to use on every problem. None of the stuff about linear independence, or rank-nullity made any sense to me until much later.

[brucepc]

I like your approach to Linear Algebra. I am relearning it after a decade or so. I just wanted to say that in the current lineup of your lectures, the Easy Nullspace Excercises seem to come out of nowhere, without any real definition of what a nullspace is or why we should care about it. I gather that the nullspace is just the set of vectors (or are they coefficients of vectors, sometimes they seem to change from one to the other) that maps to the special null vector. Anyway, as someone who teaches other stuff, I thought I'd mention it, because it seems like something that might be easy to fix in an otherwise excellent exposition.

[Hythloday]

In lecture 7e (Counting Solutions of Linear System) you spoke of 'a' linear system in terms of R3 with four unknown variables. This confused me. Here, you speak of a linear system with four unknown variables as vectors in R4 which I see clearly and understand.