I initiated operation "teach myself real analysis" for similar reasons.
I took linear algebra under circumstances similar to yours. I had only taken calculus 1 and 2, about 5 years earlier, but needed to know linear algebra to understand graduate-level economics. I was able to enroll in a course at my university, but I received almost no benefit from it. (1) The professor's accent was so thick no one could understand her. (I think she was aware of this because she did teach using power point. To date that is the only math course I have taken that used power point for the lecture notes.) Everyone in the class used the slide printouts and old tests to learn the material. (2) I ordered my textbook online and it turned out to be in Chinese. I supplemented the lecture notes (which were mainly proofs) with Wikipedia. In the end, I got a B in the course. (Booo! Why didn't I do my homework?!) Considering that I was still a little punk back then, and that I was always lost during the lectures, I'm still sort of amazed that I remember what I learned. I'm also still a little resentful that I didn't have the option of taking the course online.
I think learning linear algebra using the MIT open course will be fine. The majority of linear algebra is either straightforward or something to be memorized. The trickiest parts of linear algebra come from the proofs, but you probably won't need to memorize any proofs to use Matlab or other software.
You are welcome to PM me if you come across any sample problems you can't work. I'm in a linear algebra-based course right now so the practice is welcome. (After all, I do want to teach this stuff one day. )