## (Solution Download) If U and Ware subspaces of V define their intersection

If U and Ware subspaces of V, define their intersection U ? W as follows:
U ? W = {v|v is in both U and W}
(a) Show that U ? W is a subspace contained in L and W.
(b) Show that U ? W {0} if and only if {u, w} is independent for any nonzero vectors u in U and w in IV.
(c) If B and D are bases of U and W, and if U ? W = {0}, show that B ? D = {v | v is in B or D} is independent.

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