Linear Algebra I · Vector spaces, subspaces, sums, and direct sums
The union of two axes is not a subspace
Problem
Let $H$ and $V$ be the horizontal and vertical axes in $\mathbb R^2$. Prove that $H\cup V$ is not a subspace by exhibiting two members whose sum is not in the union.
Hint
Choose one nonzero vector from each axis.
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