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-

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

l e t W_{1}, W_{2}, \dots ., 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 \dots . \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} + \dots . + 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, +, .)