>[...] > >I've come a long way in my understanding of linear algebra using the >guides I have, but, like I've said, I'm still really unsure what my >problem is.
It's perfectly clear to me what the problem is. It's exactly what I guessed, just hearing that you were doing poorly in linear algebra - seeing your attempt at defining the two terms "independent" and "vector space" just now I'm certain my guess was correct.
Your problem is you don't know the defintions of the words. You think you know what the words mean, you don't appreciate that you need to know the _exact_ definitions, _precisely_.
There's nothing anyone can do to help you learn the definitions, you simply have to _do_ it. _After_ you know the definitions people can help you understand what they mean and how they're used. But _first_ you have to _learn_ them.
> Something tells me I may just need a little more brushing >up on a little more specific useage of the concepts, and I may be OK. >Finding a way to solve proofs might be helpful too; this is something >I generally suck at and not having all the concepts clearly seems to >only make the proofs harder.
Not having the concepts clear makes the proofs _impossible_.
The next time you want to explain what linear independence means don't say what you said in that post just now, instead say "vectors v_1, ... v_n are independent if the only solution to c_1 v_1 + ... + c_n v_n = 0 is c_1 = c_2 = ... = 0." You think that's the same as what you said. It may well be the same as what you meant, but it's _not_ the same as what you _said_ - if you could state the definition _correctly_ you'd have a _chance_ with the proofs.