I need some background knowledge on linear algebra?

Ok so I'm taking a course on linear algebra and I'm totally lost. The prof introduced all this fancy notation and concepts and I have no idea what they mean. He assigned homework for the first week, which can be found here: http://wiki.math.toronto.edu/Toronto.../10-240-a1.pdf

I don't know whether profs normally start off l algebra by talking about maps and sets, but I'd really like someone to explain all of this to me as concise as possible. If not, atleast give me a list of the concepts I should cover before tackling these math problems.