Indeed. I think one of the thing I wanted to focus on as well in this series was explaining exactly where a lot of the formulas came from. It was a great learning experience, since a lot of what I was taught was basically as you said "here is the formula for the determinant and oh look, NxN determinants can be worked out in such and such a way if you just apply this algorithm". It was super useful to decompose why that algorithm works from a visual perspective. Same thing with surface integrals.