The connection of linear algebra with geometry

Question

I started learning linear algebra from This freely available book, and in it the author says that a course in linear algebra can be very fruitful if the subject emphasizes logic in two or three dimensions(I think this means interpreting things practically, logically and/or pictorially), which he says, is not done in the book(mentioned above).
Since I want to lay a solid foundation to my understanding, I'd like to have this fruitful beginning. Is there a book that takes such an approach to it's account?