Each one learns in different ways. You need to find one that works for you.
Not all texts are equally agreeable to everybody. As you seem to struggle with the current one, make a rough list of the topics it covers and look for alternatives that cover the same ground and are easier to understand (or at least help you get a grip to help in diving into your text). Linear algebra is standard fare, I'm sure a search nets scores of free books and lecture notes. I'm partial to Treil's Linear Algebra done Wrong, but that's just me.
Take a bird's view look at a chapter, see what it is about, what it's more important results are. Perhaps try your hand at some of the easier problems. Then dig in, look at definitions. Try to figure out why the stuff is defined the way it is. Make up examples of the things defined, and non-examples (as contrast). Check any results that are proved, see how they are used. Once you've got a grip on the use and importance, check out the proof. See what it proves, make sure it checks out (proofs use the previous results, often in not-so-obvious ways, so understanding them is good training). Maybe just look at the more important results first, sort of spiraling in.
Reading math of any type is not like reading a novel. The writing is much denser, a large part of it devoted to discuss stuff that isn't obvious or known beforehand. Don't expect to advance fast. Just keep moving. If it gets too tough, look for other sources. Then, maybe, retake the thread where you left.
Do the exercises, after solving (or at least giving them a decent shot) look up solutions. Again, there are many hundreds of linear algebra courses being offered all over the world, many publish homework/exams, often with full solutions.
