Scalars and determining subspaces

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To determine if a subset of a vector space is a subspace, it must be closed under addition and scalar multiplication. As far as I can tell, this means adding two arbitrary vectors in the subset and having the sum be within the subset.

But...can the scalar be any number? Is there any limitation?
 
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If ##W## is a subspace of ##V##, then ##\alpha v\in W## for any scalar ##\alpha## and for any ##w\in W##.
 
micromass said:
If ##W## is a subspace of ##V##, then ##\alpha v\in W## for any scalar ##\alpha## and for any ##w\in W##.

Thanks, my book is terrible.
 

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