This is a presentation I gave at a math department meeting to both review necessary content for the upcoming units and get the department thinking about the deeper geometric meaning of what the calculations are doing. It was well-received so I thought I would share it. It can be scavenged for your own PD or department meeting or be a source of discussion questions for a Precalc Honors class or just for your own development as an educator. Take whatever you want from it.
I included copious notes, anticipated questions and responses, as well as in-depth explanations. The key to success is preparation. As always, my goal is to make you look like a superstar.
3X3 linear systems
row reduction, rref
connecting new material in 3D to intuition from 2D knowledge
wedge product, differential geometry