> The first lecture was using a 4x4 matrix because you can use it for a more general set of transformations, including affine transforms (think: translating an object by moving it in a particular direction).

I think this is mixing up concepts that are orthogonal to linear spaces, linear transformations, and even specific operations such as rotations.

The way you mention "more general set of transformations" suggests you're actually referring to homogeneous coordinates, which is a trick that allows a subset of matrix-vector multiplication and vector addition in 3D spaces to be expressed as a single matrix-vector multiplication in 4D space.

This is fine and dandy if your goal is to take a headstart to 3D programming, where APIs are already designed around this. This is however a constrained level of abstraction above actual linear algebra, which may be and often is more confusing.