Let W be a nonempty subset of a vector space V with vector addition and scalar multiplication O. If v, u € Wand r is a scalar, which of the following guarantees that W is a subspace of V? The zero vector and vo(r ○ u) are elements of W. W is closed under . The vectors vu and ro v are elements of W. O The zero vector and ro u) are elements of W.

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Chapter2: Second-order Linear Odes
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17. Vector Spaces and Subspaces

Let W be a nonempty subset of a vector space V with vector addition and scalar
multiplication O. If v, u € Wand r is a scalar, which of the following guarantees
that W is a subspace of V?
O The zero vector and vê(r ○ u) are elements of W.
W is closed under .
O The vectors v u and rO v are elements of W.
O The zero vector and r O (vu) are elements of W.
Transcribed Image Text:Let W be a nonempty subset of a vector space V with vector addition and scalar multiplication O. If v, u € Wand r is a scalar, which of the following guarantees that W is a subspace of V? O The zero vector and vê(r ○ u) are elements of W. W is closed under . O The vectors v u and rO v are elements of W. O The zero vector and r O (vu) are elements of W.
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