The SHOCKING truth about determinants [SIQA-16-full]

Error at 10:40: Should be -2*w_x*v_y

Context:

I recently wrote an article about how to code rational arithmetic in
Erlang (link below). In the article, I mentioned that the criteria
for two rationals a/b and c/d to be equal is if ad - bc = 0. Which is
a determinant.

Cannon and I were talking about this in a chat, and recorded this
short episode where I explained the connection.

Cannon understands the interpretation of the determinant as signed
area. He is dimly aware of the interpretation of the determinant as
describing whether or not a system of linear equations is invertible.
Although I have never sat him down and explained the connection in
full. I explained that connection quite clearly in my "Gaussian
Elimination, Determinants, and Invertibility" playlist (link below).

I did previously explain some of the determinant ideas in Episodes 9
and 10, particularly the link between determinants and quaternions.
That is (you guessed it) linked below.

My plan is to explain all of this linearly in the "Foundations of
QAnal" series of blog posts (link below) and in the "Math for
Programmers" playlist (link below).

00:00 The determinant as signed area
14:00 Cross product
16:00 Browsers
21:20 The connection with rationals
24:00 zx's ratio problem
32:00 Rational parameterization of the circle and doing exact rotations
41:20 Why math is beautiful

Rational parameterization of the circle GeoGebra: https://www.geogebra.org/m/a4dea8xp

[blog series] Foundations of QAnal: https://zxq9.com/archives/category/foundations-of-qanal

[prior episode] Episode 9.1: https://rumble.com/vougyu-niffers-wokism-and-craig-cannons-girthy-hose-problem-siqa-9.1.html
[prior episode] Episode 9.2: https://rumble.com/vovq9o-craig-cannon-reacts-to-revelations-16-siqa-9.2.html
[prior episode] Episode 9.5: https://rumble.com/vp5mwk-the-ladies-love-qanal-siqa-9.5.html
[prior episode] Episode 10.3: https://rumble.com/vphm3w-the-founders-record-breaking-discovery-about-quaternions-siqa-10.3.html
[playlist] Gaussian Elimination, Determinants, and Invertibility: https://odysee.com/@DoctorAjayKumar/gedi
[playlist] Math for Programmers: https://odysee.com/@DoctorAjayKumar/mfp