Hi can some one please verify that my work is correct for this, its really important that I get this right.

So we call the set W then

since its not closed under addition so itsnot a subspace, and I did not bother to check the other axioms but I believe it should be closed under scalar multiplication. Also of course its not empty since (0,0) is in the set

so it basically failed the closure under addition axiom thus making it not a subspace.

Is this solution correct and sufficient