I can't say whether or not it is the standard approach but I do know that it is very common in many countries to teach a linear algebra course that is heavy on matrix operations, that you can come away believing that linear algebra is somehow _about_ matrices and their operations. I know many in my university class seemed to believe that.
A book I enjoyed is Axler's Linear Algebra Done Right[0], in which, if I remember correctly, doesn't contain a single matrix.
A book I enjoyed is Axler's Linear Algebra Done Right[0], in which, if I remember correctly, doesn't contain a single matrix.
[0]https://zhangyk8.github.io/teaching/file_spring2018/linear_a...