Having read a couple of books on the subject, I really think this is an ideal choice for any introductory Linear Algebra course. Poole's emphasis is clearly on readability for a range of students and building intuitive understanding on a vector-based foundation (where other texts have you lose sight of this through endless computations and sets of matrices). He provides intermittent examples of appropriately rigorous proofs without inundating you (lets you fill in the details in a few exercises) and always offers techniques to help you practically approach types of problems. I'm not a hardcore mathematics person - mostly taking these courses to fill my requirements for teaching high school physics - but I can honestly say that you can carefully read through a section once, and blaze through many problems that are on par with most other texts' (Poole, thankfully, is very generous with # of medium-level practice exercises, and carefully selects challenge problems that are enlightening but still in the scope of the book!). Just as a heads-up, this book doesn't always use the "classical" LA terminology (example: Chapter 5 doesn't emphasize that it is actually dealing with "the Fundamental Theorem of Linear Algebra"). However, it doesn't skimp on any vital intuitive/conceptual implications these theorems bring to light...

Ultimately, this book retains value even after you finish the course (keeping it, when I have the time to go through the entertaining professional applications of LA the author shows in detail). I would seriously consider buying books by this man if he published on other subjects, even if I didn't necessarily need the course!