hello, we just started learning about vector spaces in my linear algebra class and i'm a little confused. I was wondering if someone could give me a link to a good study guide if there is one or if i could get some help doing some examples. i think my problem is i need more examples because the chapter in my book is lacking those in this chapter. I'm going to start with determining vector spaces.

here's an example of what i'm trying to do:

Let V=$\displaystyle R^2$. Define $\displaystyle \oplus$ by (x,y) $\displaystyle \oplus$ (t,s)=(x+t,y+s) and $\displaystyle \odot$ by c $\displaystyle \odot$ (x,y)=(cx,c). Is V with $\displaystyle \oplus$ and $\displaystyle \odot$ a vector space?

I know i'm supposed to use the 10 rules to figure this out but i'm not sure exactly how i'm supposed to go about doing that. any help would be appreciated.