Math Help Forum: Vector space with componentwise..

Let


a) With the standard componentwise operations show that V is not a vector space.
b) If addition and scalar multiplication are defined component wise only on the first two components and the third is always is 1, show that V is a vector space.

You have a list of properties a vector space must satisfy. You won't have to go far down the list to find one that is not satisfied by (a). You have to check that (b) satisfies all of them. That's all there is to it.