3b1b’s Essence of Linear Algebra videos on YouTube do the best job I’ve ever seen of explaining the intuition and motivation for linear algebra and matrices. They aren’t a complete course in and of themselves. For that you’d need a textbook. But having learned LA the traditional textbook way and then watching the 3b1b videos a decade later, I would strongly encourage you to watch his videos first before opening a textbook. Once you understand the intuition, the stuff you read in textbooks makes a lot more sense and are much better motivated.

Math is about concepts, structures, and relationships. It’s not about definitions and theorems. We use those only to formalize the concepts that we’ve thought of. That’s why I recommend the “intuitionist” approach for learning math. You can fill the computations and proofs later.