In most mathematics programs linear algebra is taken in the first or second year, following or along with at least one course in calculus. While the location of this course is stable, lately the content has been under discussion. Some instructors have experimented with varying the traditional topics, trying courses focused on applications, or on the computer. Despite this (entirely healthy) debate, most instructors are still convinced, I think, that the right core material is vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Applications and computations certainly can have a part to play but most mathematicians agree that the themes of the course should remain unchanged.
Not that all is fine with the traditional course. Most of us do think that the standard text type for this course needs to be reexamined. Elementary texts have traditionally started with extensive computations of linear reduction, matrix multiplication, and determinants. These take up half of the course. Finally, when vector spaces and linear maps appear, and definitions and proofs start, the nature of the course takes a sudden turn. In the past, the computation drill was there because, as future practitioners, students needed to be fast and accurate with these. But that has changed. Being a whiz at 5×5 determinants just isn’t important anymore. Instead, the availability of computers gives us an opportunity to move toward a focus on concepts.