Why would you want to teach "every well behaved function has a family of linear functions associated with it" before you teach how to work with linear functions?
CCSS.MATH.CONTENT.HSN.VM.C.6
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
CCSS.MATH.CONTENT.HSN.VM.C.12
(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Math education gets a bad rap in the USA, because anything that students don't remember learning, is claimed to have never have been taught. And that is just not true. Math teachers aren't as dumb as people pretend they are.
The word linear is never used in that part of the standard, nor is any relationship to calculus expressed explicitly (and there is not really any relationship to anything else, just saying that a matrix can be used to express incidences in a network is useless if they never study networks). Probably because calculus is not part of the CC standard, which is my point exactly. Besides, Common Core is not what most living people in the US experienced in school.
I have seen the standards for high school math teachers and trust me, they are low. Most of my classmates in undergrad (which was supposed to be an excellent program for math teachers) are now high school teachers. Their complaints about how much they hate basic linear algebra and "just want to be done with it so they can go teach high school" are still ringing in my ears.
