The sum of subspaces is a subspace

Created almost 9 years ago, updated about 8 hours ago

If $x=u_1+w_1$ and $y=u_2+w_2$ belong to $U+W$, then $ax+by=(au_1+bu_2)+(aw_1+bw_2)$ also belongs. Zero is included. Thus $U+W$ is a subspace, unlike a general union of subspaces.

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