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Is the set $\{(x_1,x_2,x_3,x_4)|x_1x_2x_3x_4=0\}$ a subspace of $\mathbb{R}^4$?
In general, how do I show this? I'm aware of the stability criteria, but I'm not entirely comfortable with them.
In the comments below, I was advised to look at the vectors $(1,0,0,0)$ and $(0,1,1,1)$. Their s...