If I were to teach linear algebra I would stick to the 3D graphics approach. Maybe as far as including labs for implementing a ray-tracer.

It is just the most fun, intuitive and eye opening application of basic linear algebra.

Don't forget the fun!

Data science applications can come later.

I didn't go to university for CS. Instead I did physics. Because of that, learning/remind myself of this stuff was relatively easy, and so I did it.

And let me tell you, it didn't actually made me a better data scientist/model builder, for the same reason that learning how to implement some tree traversal didnt make me a better programmer.

This seems to be a more hands-on linear algebra intro, starting with matrices and building up from there. Note I've not actually read the whole thing, just skimmed it.

Something similar worth looking at is: https://ocw.mit.edu/courses/18-065-matrix-methods-in-data-an...