I have a lot of thoughts on this from my own personal experience and was honestly surprised to find that it was "Linear Algebra" that was the class being discussed -- I thought I was the only one who suffered through that!

This was 20 years ago, for me, and my experience was nearly identical. I was not a great student in High School but ... now having to pay for my own classes ... did well in every class in college except for this one. I attended sessions with tutors offered through my class, I attended office hours, I failed ... hard. The pattern I kept running into was one of learning the material after the exams for each unit were returned to me. In fact, it was so ridiculous, I stopped going to class, resigned to the fact that I was going to fail and simply showed up for the exams. I re-took the class and managed a near-4.0 on the same material. The school I attended had a bad reputation among its math department as being ridiculously difficult staffed with professors who had a basic understanding of English. Of course, this came from students who had recently failed, and they'll have the loudest and often most defensive voices on the subject.

None-the-less, out of the three professors, two were in the "avoid" category pretty quickly due to feedback I received about how difficult it was to understand the words they were speaking[0]. The third was a recent hire -- the rumor being that they picked someone from the US because of the frequent complaints about understanding the set of maths professors they currently employed. But I suspect a lot of people played the game of "pick the guy with the American sounding name" and found out the same thing that I did -- a deep south Alabama accent is much farther from English as it is spoken where I live than any ESL professor's native accent. I picked up about every fifth word coming out of this gentleman's mouth with his very thick drawl and unusual word choices and lousy grammar. In the north, we'd be surprised to find out that he's a maths professor, stereotyping him as a farmer

I suspect, after reading this, that there was more to it than just my struggling to understand what was being said. My pattern was that despite all of the extra energy put into attending tutoring sessions and scheduling office hours, I found myself understanding the material just after we'd taken an exam on the portion we were studying. As this was too long ago, I don't remember if we were given solutions or not, but it fits with that pattern -- the tests were reviewed pretty thoroughly after they were taken and I could see what I did wrong -- it clicked. It clicked so much that despite getting a hard fail in the class, I ended up sailing through with -- I think -- a 4.0 or somewhere near the second time around, attending only on exam days -- with the same professor.

The tutoring/office hours which are brought up as "the way you teach without the solution" were totally inadequate. The staff provided for assistance were not professors, or even particularly skilled tutors. They were advanced maths students who found the work being done to be easy and didn't know how to teach things that were very basic to them. Open office hours were difficult for me to get because I had a full-time job in the field I was seeking my degree in; they were always booked and by the time I knew I needed them, the earliest I could meet with the professor was after the exam. I ended up just scheduling them as soon as I was allowed and cancelling if I didn't need it. Many, many others did this -- it resulted in a group forming by the smallish meeting space that he reserved for these[1] in hopes that he'd finish early and grab the first student waiting. I never did this, but on days that I had a formal appointment, I'd noticed the waiting students would sit on the floor with their materials trying to help one another -- it was a blind-leading-the-blind scenario.

And here's the worst of it: I'm not bad at math! This class made me fear every future maths course I had to take. I got through two Calculus classes many years later due to a desire to fill in the gaps I had learned from books -- they were easy by comparison. I think the way it was taught was specifically because it's a class that many fear; we were gently introduced to the concepts and they covered much less by comparison than linear algebra covered. They were also taught from a more practical standard -- while we were working with odd terms, functions, formulas and theory, they were often brought back to "and here's where it applies in engineering/life" which made it a lot more interesting. The problems we faced in linear algebra, despite having many interesting practical applications, were rushed through and were taught as though "this is just something that Maths majors learn so that they can fill whiteboards for use as props in movies and The Big Bang Theory to make the characters look smart".

My experience in higher education was, in general, not a good one. I left this school a semester later and went elsewhere mostly because of this class, though the final nail in the coffin was an experience in my first programming class[2] where a test -- with very few answers -- responsible for half of the grade had a bug in it -- a failure to dereference a pointer ... a missing star, caused more than half of the answers to be "F - None of the above" or didn't have an answer. I chose to treat the unanswerable as "undefined behavior" (it was C, after all). Luckily, in an attempt to provide answers that might "look right", I found that if I pretended the function call didn't exist, I'd find an answer among the choices and explained to the professor that my fictional compiler optimized away the call since there wasn't an answer among the list that worked without it. I spent an hour arguing with the guy but he ended up re-scoring it to perfect.

[0] One was Indian, the other was Pakistani and I know I would have done better with either of them given that I worked with folks from those regions regularly who had pretty thick accents; like anything, you learn to understand the phrasing and tempo and you stop hearing the accent pretty quickly. I suspect many of the younger students coming from American high schools struggled having encountered it for the first time. It's nothing on the professors or their country of origin, though.

[1] I have never visited a professor for "Office Hours" outside of this class; I don't know if it was because this professor was on his first semester at my school or if this is common but no part of it had the scent of "open office hours" -- it was done in a conference room about the size of my kid's bedroom with a single round table and four chairs cramped under it, one of which couldn't be pulled out due to its proximity to the wall. The professor tended to explain things while searching for materials to help me ... that he didn't have on him that day, so he'd scribble on a piece of paper.

[2] I agonized over this during the 45 minutes we had to finish the exam. Worse, it was proctored by a TA or assistant -- someone I'd never seen, before, and not someone who would know if it was a mistake on the professor's part or not. I'm also pretty sure the guy was playing Descent on the laptop he sat in front of while the test was being taken. It was pure luck that I found a way to answer the questions accurately which also could be defended when an accurate answer wasn't a choice. My concern was that by ignoring the bug, had the professor intended it, I'd have no defense that wouldn't sound like "I didn't notice it and now that I know I got it wrong, I'm trying to weasel my way to a better grade". It was still a tough hill to climb.