[Grustaf]

Sure, linearity is a very useful concept, but very few high schoolers are able to understand such concepts in the abstract, which is when it's the most useful.

I remember when we were introduced to abstract vector spaces in high school, and we were all pretty confused, even though this was a high school dedicated to mathematics, the foremost in the country.

Even complex vectors had us scratching our heads, which in retrospect seems absurdly trivial. It's just that we were used to thinking in very concrete terms, anything purely abstract is 10 times harder to grasp, so you probably can't teach things like linear transforms without matrices.

Derivatives and integrals on the other hand are very easy to visualise.