Comment by bandrami

Bingo. We did matrices in high school and even through a first linear algebra course in undergrad I got more or less competent at the mechanics of matrix multiplication without ever having any sense of why anyone would want to do this or why these rules, as opposed to some other set of rules that were equally formally valid, were of any interest. I could even tell you what the eigenvectors of a matrix were but had no sense of what that actually meant in terms of a linear transformation that matrix represented. Linear algebra is probably the area of math that is both universally important and completely skimped on by our education system.