You certainly were lucky to be taught Linear Algebra in such a manner! I came to understand the importance of such an approach only after a lot of head-scratching and self-study. IMO, a beautiful and important branch of "Practical" Maths has been needlessly obscured by the pedantic formalism espoused by the teaching community. Linear Algebra SHOULD always be taught alongside Coordinate/Analytic Geometry and Trigonometry for proper intuition.

I found the book "Practical Linear Algebra: A Geometry Toolbox" very helpful in my study.