How would you prove that adding two vectors in the column space would result in another vector in the column space?(adsbygoogle = window.adsbygoogle || []).push({});

I know this is maybe the most basic property of vectors and subspaces, and that the very definition of the column space says it's spanned by vectors in the column space. Is there any way to prove this, though?

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# Proving vectors are in the column space

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