Showing that linear subset is not a subspace of the Vector space $V$ I am given the following
$V = \mathbb R^4$
$W = \{(w,x,y,z)\in \mathbb R^4|w+2x-4y+2 = 0\}$
I have to prove or disprove that $W$ is a subspace of $V$.
Now, my linear algebra is fairly weak as I haven't taken it in almost 4 years but for a subspace to exist I believe that:
1) The $0$ vector must exist under $W$
2) Scalar addition must be closed under $W$
3) Scalar multiplication must be closed under $W$
I don't think the first condition is true because if I were to take the vector, there is no way I can get the zero vector back. Is that correct or am I doing something very wrong?

I feel I should indicate that condition 2 and condition 3 fails as well. The vector $v = (2, 0 , 0 , 0)$ belongs in the subset, but neither $2v$ nor $v+v$ belongs in the subset.
It is thus not a subspace.
