$W$ is not a vector subspace of $R^3$.
Work Step by Step
Let $u=(1,1,-1), v=(1,0,-1)\in W$. Since $$u+v=(1,1,-1)+(1,0,-1)=(2,1,-2),$$ then $u+v$ is not an element of $W$ and $W$ is not vector subspace of $R^3$.
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