Prove the theorem. A non empty subset W of a vector space V(F) is the subset of V if and only if αW_1 +βW_2 ∈W ∀α,β ∈ F and W_1 ,W


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Question Number 210297 by Spillover last updated on 05/Aug/24

$P r o v e t h e t h e o r e m .$ $A n o n e m p t y s u b s e t W o f a v e c t o r s p a c e V (F)$ $i s t h e s u b s e t o f V i f a n d o n l y i f$ $α W_{1} + β W_{2} \in W \forall α, β \in F a n d W_{1}, W_{2} \in W$
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