It's hard to convince kids why they should learn advanced abstract math, beyond what is necessary to calculate the tip on a restaurant bill. The number of high school students who will use advanced math beyond high school is very small, but those that do will have high impact, which is both in society's interest and their own interest as high earners.
The kids that study and apply themselves, I don't think it's so much that they can see they understand the benefits of linear algebra at the time, it's that their parents and the social network they're a part of sends them signals that this is what they should do to be successful and they're rewarded for doing well in school.
The kids that study and apply themselves, I don't think it's so much that they can see they understand the benefits of linear algebra at the time, it's that their parents and the social network they're a part of sends them signals that this is what they should do to be successful and they're rewarded for doing well in school.