Prove-the-theorem-A-non-empty-subset-W-of-a-vector-space-V-F-is-the-subset-of-V-if-and-only-if-W-1-W-2-W-F-and-W-1-W-2-W-

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