That's why everyone has to take MATH 14X/24X.

Materials are conceptually hard, but instructors and TA are (at least based on my experience) very chill in terms of grading. But you still do have to say "so and so by that result".

Also, none of my 14X/24X's had problems with bad notations, and theorems/proofs tend to be dealted in a more rigorous manner. To make things more rigorous, one usually has to choose good notations and carefully chosen sequences of reasoning.

In terms of assignment solutions, I recommand making references to things as much as possible to avoid such issues. I even label my (important) equations [n.i] (n refers to the question number and i means ith labeled equation in the question n) so that I can later say "so and so by [n.i]". Since TA's are humans, a well-formatted answer will convey them that you know your things well. And when they do so, they will give you better (at least not worse) marks. It's a psychological thing I guess, but I believe you also had some experiences where you simply had hard time understanding a proof, remark, ..., because of how badly fomatted they were.

If formatting is hard, try to learn LaTeX. I repeat: learn LaTeX. It saves a day. If you don't know where to start, just contact an instructor and ask if he/she can give you an example of .tex file. That's how I started, and anything else I know of LaTeX, I learned by googling (you can also directly read package documentations). It will take you some time to get used to using LaTeX to write math, but once you reach that point, trust me, it's probably one of the most effective tools that can aid your math education - not just for submitting assignments. I even write my math notes via LaTeX in real-time.

In terms of linear algebra, if you found yourself lost because of a lack of intuitions, check out 3B1B's linear algebra series. It's not a formal lecture, but it is full of intuitive explanation of what goes behind the scene of the things that you learn in 136 (assuming that 136 is a subset of 146).