I suppose you would have to programme this, because I couldn't find anything relating to vector spaces in my Maplesoft Linear Algebra tutor or package.

My question really is, you have a problem like, the set of all pairs of real numbers of the form (1,x) with the operations (1,y)+(1,y')=(1,y+y') and k(1,y)=(1,ky) 

( ^ taken straight out of my homework haha)

and you run through the 10 vecctor space axioms to determine whether it fails and it not a vector space, or it passes all and it is a vector space.

Is there a way to do this in Maplesoft?