Sometimes a subset of a vector space is itself a vector space (with respect to the linear operations already given). Consider, for example, the vector space and the subsets consisting of those vectors for which
(a) is real,
(c) either ,
In which of these cases is a vector space?
Not a vector space since multiplication by a scalar yields .
is not in .
Is a vector space if . If I think of this in terms of , I would have the plane if I'm not sure if I should be thinking like this..
Again, if I think of it as , I would get the plane and the plane.
This is not closed under addition, ,i.e., not a vector space.
I do not see which axiom for a vector space is violated though..
Is a vector space.
Hm, I would say no since it looks like it's not closed under addition.
Sorry for my pathetic attempts, can't do much better..