It that all it is, or am I misunderstanding. Everybody seems to think that this field of math is very important, I feel like I should know it by now.
You are correct that the fundamentals (Vectorized computation, aka matrices) are often introduced early on. The level at which you interface with linear algebra often scales with the level of math you are at. You can add them , integrate them , and use them to solve some PDEs . You can see how all these "levels" of linear algebra would be accompanied by another math class pushing you to utilize linear algebra at a higher level than before. It appears that you're at the first level. I've actually never done  in the classroom, but  was introduced to me in a class on differential equations that utilized matrices as a possible solution route.
If you are interested in learning more, Khan academy has good linear algebra videos.
See MIT OCW Scholar's Linear Algebra offering: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algeb...
Take a look at the final exam and see if it seems like something you've seen. If not, I strongly urge you to consider studying the subject.
A book that shows linear algebra's applications at a more advanced level is Strang's Computational Science and Engineering: http://math.mit.edu/~gs/cse/
I don't know about UK curriculum but the colleges in USA like MIT/Stanford/Princeton/etc have courses focusing on linear algebra (matrix math). Example:
One of those classes is often taken as an elective to meet one of the math requirements for graduation.