I just recently discovered an awesome visual intuition for what a determinant is, and why one cannot solve a linear system with a zero determinant. I'd love to contribute to this!
In 2 dimensions, the absolute value of a determinant of a matrix is just the area of the parallelogram subtended by the row vectors of the matrix. If this area is zero, it means that the vectors are co-linear. And of course the intersection of co-linear vectors is an infinite set (in R^n anyways). The same idea holds in higher dimensions, with the 3d case being similarly possible to visualise (as a volume). Since the unique solution of a linear system is the point at which a bunch of lines/planes/hyperplanes meet, a zero determinant implies a zero area which means that at least two vectors are coincident and hence there are infinitely many solutions.
my opinion, the lack of comments come from that the site isn't very intuitive for knowing what this is all about. maybe just a clean description or use case scenario is in order.
Admittedly the first sentence in the README.md points to relevant information (http://setosa.io/ev/) However, yes, they should have included the one sentence description on that page it links to in the README.md itself.
Explained Visually (EV) is an experiment in making hard ideas intuitive inspired the work of Bret Victor's Explorable Explanations. See http://worrydream.com/ExplorableExplanations/ to learn more about Explorable Explanations.
I upvoted without commenting because I love EV, highly appreciate the free release but had nothing to say. Random praise is just noise that can be expressed by upvoting.
These are awesome and kudos for open sourcing it, this is the kind of material I expected all school kids to be learning from by now (based mostly on sci-fi).
