[gizmo686]

My point was not that someone would not be motivated to learn the abstraction, it was that the abstraction would not make sense without a reason to use it. That reason could very well be an entirely theoretical application, but why would the concept of expressing a linear equation as a matrix make any sense to someone who has never dealt with more than 2 linear equations at a time?

[adeelk]

Sure, but verroq was talking about vector spaces and linear maps, not matrices. The theory of vector spaces over a field is more general and can be applied to much more than systems of equations.