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

1. ## 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.

Please, help. Thank you.

2. ## Re: Determine whether W is a subspace of the vector space?

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.

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

3. ## Re: Determine whether W is a subspace of the vector space?

Thank you very much for your prompt response.

I forgot that cu + cv has to be in W as well.

Thank you again.