Using the determinant to calculate polygon areas, and the heart of mathematics | Abstract Algebra 11

This is the climax of my "untying knots in linear algebra"/"wtf is the determinant" mini-series.This is the video I've been building up to. There's more I want to talk about before moving on in Artin. Also contains a bonus rant with a preview of what's to come.

Correction at 11:18: I should have made an edge going vertically down to the x-axis, and then another edge on the x-axis going back to the origin.