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Is the empty set is a subspace of any vector space?

im not too sure about this one, is the zero vector in the empty set?

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    $\begingroup$ As you say, the empty set does not contain the zero vector, and so it is not a vector space. $\endgroup$ – Prahlad Vaidyanathan Apr 27 '14 at 11:57
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The answer is no. The empty set is empty in the sense that it does not contain any elements. Thus the zero vector is not a member of the empty set.

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