Hey,

Consider a subset $\displaystyle W$ of a vectorspace $\displaystyle V$. If I can show that $\displaystyle W$ is a subspace of $\displaystyle V$ would that imply that $\displaystyle W$ itself is a vectorspace?

Or do I have to go the other way and first show that the subset $\displaystyle W$ fullfills the conditions of a vectorspace and therefore is a subspace.

Cole someone kindly clarify.

Thanks.