Prove that If W is a subspace of a vector space

killjoy1990xb9 2022-01-04 Answered
Prove that
If W is a subspace of a vector space V and w1,w2,,wn are in W, then a1w1+a2w2++anwnW for any scalars a1,a2,,an.
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Linda Birchfield
Answered 2022-01-05 Author has 39 answers
Here W is a subspace of a vector space V and w1,w2,,wn are in W.
From above, w1W,w2W,.,wnW.
Since, W is closed under scalar multiplication a1w1W,a1w2W,.,a1wnW for any scalars a1,a2,,an.
W is closed under addition.
Hence, a1w1+a2w2++anwnW for any scalars a1,a2,,an.
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Suhadolahbb
Answered 2022-01-06 Author has 32 answers

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