$W$ is not a vector subspace of $R^2$.
Work Step by Step
Let $u=(2,4), v=(3,9)\in W$. Now, $$u+v=(2,4)+(3,9)=(5,13).$$ Since $13\neq 5^2$, then $u+v$ is not an element of $W$. Hence, $W$ is not a vector subspace of $R^2$.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.