
Vector Space help!
Hi, I have trouble understanding vector space and how to determine whether something is a vector space or not. I am having trouble with these problems.
Determine whether the set, together with the indicated operations, is a vector space. If not, identify at least one of the ten vector space axioms that fails.
1) M sub 1,1 ( I guess it's a matrix 1x1?)
2) the set of all fifth degree polynomials with the standard operations
3) the set of all first degree polynomial functions ax+b, a is not equal to 0, whose graphs pass through the origin with the standard operations.
Please help. Thank you.

Vector spaces are closed under addition, which should help you dispose of (2) and (3).