If W is a nonempty subset of real vector space 3 using the same operations, then W is a subspace of 3 if and only if:

1
W is not closed under scalar multiplication but closed under vector addition in 3
2
W is closed under vector addition and scalar multiplication in 3
3
W is not closed under vector addition but closed under scalar multiplication in 3
4
W is neither closed under vector addition nor closed under scalar multiplication in 3

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