Should I solve all the problems in each set problems after each section on the textbook ?
From my experience, that's up to you. The homework is there to help you. Mathematics tends to build upon itself also, so we cannot forget that if we don't master a certain topic now, we might need it later. In that case, then a person is trying to learn new things, and old things at the same time. Math majors don't always get much of a life, at least ones who get good grades in challenging courses. It is a very time consuming subject, and part of the reason calculus is taken before linear algebra, is to prepare the student for rigorous material. I say, do as much as you can, do a lot of problems, but you don't necessarily have to do them all. If you get stuck, move on. Ask questions. It takes a lot longer to stop and catch your mistakes without the help of others.
usually by solve them you can improve your knowledge, but occasionally some of problems are not good and they are not applicable .
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