$\{(x, y, z)\} \space$ with $\space x + y + z = 0$
Working through some problems in a textbook and I'm not very confident about checking if subsets are subspaces. I know that for a subset to be a subspace of $\space \mathbb{R}^3 \space$ it must be closed under addition and scalar multiplication but I'm not sure how to check this with examples. Any help would be appreciated!