You might work yourself through the exercises in "baby Rudin" to learn analysis, and ask questions on Stackexchange, but it'll probably often be very frustrating.

I think there are so many great books on linear algebra, that it is difficult to single one out. I think LA is also picked up much easier by most people, especially with a programming background.

It isn't really about the book imho, it's about being disciplined and do some practice exercises every day, like you're training a muscle.

Edit: and I recommend you never consult solutions, except to verify yours. "Illusion of competence" is a big thing you might accidentally step into in mathematics. My experience is that looking up solutions gives you a short strong eureka feeling, but you learn almost nothing from it. You have to go and arrive there yourself.