(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let U and W be subspaces of a vector space V

Show that the set U + W = {v ∈ V : v = u + w, where u ∈ U and w ∈ W} is a subspace of V

2. Relevant equations

3. The attempt at a solution

I understand from this that u and w are both vectors in a vector space V and that u+w is a vector in a vector space V but I'm not sure how to apply the rules to this problem in order to show that U + W is a subspace of V

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# Algebra - Proving a subspace

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