How does linear algebra compare in difficulty to calculus?

it depends what level of linear algebra the course is. some elementary linear algebra classes are very computational and hence on about the same level as a calculus class. however the 2 courses i took in LA were pretty theoretical and proof based- (i'd say about 40% theoretical for the first one i took and 60% for the second one). in my opinion, it can be considered slightly more difficult than the calculus 1-3 sequence as it requires a certain "mathematical maturity" to really digest and understand the material so you can apply the theory to do many different types of proofs. if you are considering taking this course in the future i would recommend that you take calculus 1-3, and an intro to proof writing class as prerequisites. also, linear algebra does deal with 2 and 3 dimensional spaces, but actually generalizes certain concepts and theory to "n" dimensional spaces- i.e. the 128th dimension. however, it is a really useful and interesting area of mathematics.

Seeing as how you are currently in Pre-Calculus/Trigonometry, it all depends on what you think of the class that you are in right now. Although I have not taken the "Linear Algebra" class, I can parrot what I've heard: it deals with a third dimension, which can be tricky. If you proceed on what my high school would consider to be the "normal" path, you should take Calculus AB (or BC) next year. I'd say Calculus AB would be the easiest, then linear algebra, and finally Calculus BC would be the hardest.

For those who are unsure what the AB and BC mean: There are three main parts of Calculus (A, B, and C). The AB class covers only the first two sections, while the BC class covers the entire book (or, if you are picky, the last two sections). I am currently in Calculus BC and I can tell you that the AB class learns in a year what the BC class would learn in the first semester. Anyway, after AB, the student would move on to BC, and later move on to Calculus 3 and Differential Equations (or other classes, it all depends on your school). If you are a math person, you should continue on with Calculus ESPECIALLY if you aspire to be something that requires "intense" mathematical computations.

Lastly, before I end this, I want to add one more thing: If you are thinking about taking Physics next year, then you should definitely take Calculus (BC, preferably). The reason is simple: So far this year, my BC class has been *nearly* the same material (certain chapters, at least) so that of Physics. By taking both classes, you'll form a MUCH better understanding of the two subjects (rather that if you were to take them separately).

I really hope this helps you make your decision!