I've learned linear algebra course quality varies substantially. One acquaintance whom I met after they graduated a big university in Canada reported having to do things like by-hand step-by-step reduced row echelon form computations for 3x4 matrices or larger. I had to do such things in "Algebra 2" in junior high (9th grade), until our teacher kindly showed us how to do the operations on the calculator and stopped demanding work steps. If we had more advanced calculators (he demoed on some school-owned TI-92s, convincing me to ask for a TI-89 Titanium for Christmas) we could use the rref() function to do it all at once.

In my actual linear algebra class in freshman year college we were introduced to a lot of proper things I wish I had seen before, along with some proofs but it wasn't proof heavy. I did send a random email to my old 9th grade teacher about at least introducing the concept of the co-domain, not just domain and range, but it was received poorly. Oh well. (There was a more advanced linear algebra class but it was not required for my side. The only required math course that I'd say was proof heavy was Discrete Math. An optional course, Combinatorial Game Theory, was pretty proof heavy.)