1. let V be a vector space, U1,U2,W subspaces.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Vector Spaces questions.

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