# Determine whether W is a subspace of the vector space?

• July 3rd 2011, 09:45 AM
Jav
Determine whether W is a subspace of the vector space?
W={(x,y): y=ax, a is an integer}, V=R^(2)

It is not a subspace of V, but I can't find an example, where this is not valid.

• July 3rd 2011, 09:50 AM
Isomorphism
Re: Determine whether W is a subspace of the vector space?
Quote:

Originally Posted by Jav
W={(x,y): y=ax, a is an integer}, V=R^(2)

It is not a subspace of V, but I can't find an example, where this is not valid.

$(1,2) \in W, (1,3)\in W$. But does $\frac12(1,2)+\frac12(1,3)$?