1. let V be a vector space, U1,U2,W subspaces. prove/disprove: if V=U1#U2 (where # is a direct sum) then: W=(W^U1)#(W^U2) (^ is intersection). 2. let V be a vector space with dimV=n and U,W be subspaces. prove that if U doesnt equal W and dimU=dimW=n-1 then U+W=V. for question two, in oreder to prove this i need to show that dim(U+W)=dimV which bassically means that: dim(U^W)=n-2, but how do i prove this? for the first question i think it's correct but i dont know how to prove it, any one has got any hints for me, thanks in advance.