- #1

- 32

- 6

I'd like to have a little insight about why the determinants of ℝ

^{2x2}and ℝ

^{3x3}matrices are computed that way.

I know how to calculate said determinants in both the cases and I also know what's the meaning behind it thanks to "3blue1brown"'s youtube channel, which states that they are a scaling factor respectively to the area of a surface in ℝ

^{2}and of a volume of a parallelepiped in ℝ

^{3}, but what's the connection between, as in the simpler case, the scaling factor of an area in ℝ

^{2}and it being computed as

**ab - cd**? (Say the matrix is [a c; b d] meaning "a c" is the first row).

What's the geometric intuition or derivation?

I thank everyone who'll partecipate in this thread in advance.