I think it was a brilliant and evil trick by the linear algebra folks.

Start the path at calculus. Naturally, this will lead to differential equations. Trick the engineers into defining everything in terms of differential equations.

The engineers will get really annoyed, because solving differential equations is impossible.

Then, the mathematicians swoop in with the idea of discretizing everything and using linear algebra to step through it instead. Suddenly they can justify all the million-by-millions matrices they wanted and everybody thinks they are heroes. Engineers will build the giant vector processing machines that they want.

Ha, Ha, True dat :-)