There are several aspects that contribute to the decision to invest quite a lot of time on linear algebra before introducing abstract algebra. Firstly, there is the historical aspect. Linear algebra came first, and groups, rings and the rest of the gang came (considerably) later. read more
In the university curriculum I went through, Linear Algebra was one of the first-year courses, usually a prerequisite for everything else. Abstract Algebra can mean different content - it could be Galois Theory, or it could be formal theory of algebraic structures, for example. How hard the course is depends entirely on the lecturer. read more
Linear algebra services numerous fields and while abstract algebra is certainly of great importance, it can be argued (successfully) that linear algebra equips one with plenty of immediate tools for use in many areas. read more
Linear algebra is a fundamental departure from other kinds of math you would have taken in the past, so there's no reason to be surprised you find it a challenge. read more