If I have a set of equations $x + y = 0$ and $x - 2z = 0$ how do I prove these are closed under addition and closed under scalar multiplication?
2026-03-28 03:58:46.1774670326
Proving a set of equations is a subspace of $R^3$
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The set $U$ described by the two equations is given by
$U=\{t(2,-2,1): t \in \mathbb R\}$. I think that is now easy to prove that $U$ is a subspace of $ \mathbb R^3$.