let W_1 ,W_2 ,....,W_n be subspaces of a vector space V over a field (F,+,.) prove that: (1) W_1 ∩W_2 ∩....∩W_n a subspace of the vector space V over (F,+,.). (2)W_1 +W_2 +....+W_n is subspace of the vector space V over (F,+,.)


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Question Number 88552 by M±th+et£s last updated on 11/Apr/20

$l e t W_{1}, W_{2}, . . . ., W_{n} b e s u b s p a c e s o f a v e c t o r$ $s p a c e V o v e r a f i e l d (F, +, .)$ $p r o v e t h a t :$ $(1) W_{1} \cap W_{2} \cap . . . . \cap W_{n} a s u b s p a c e$ $o f t h e v e c t o r s p a c e V o v e r (F, +, .) .$ $(2) W_{1} + W_{2} + . . . . + W_{n} i s s u b s p a c e o f t h e$ $v e c t o r s p a c e V o v e r (F, +, .)$
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