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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector Spaces questions.

**Physics Forums | Science Articles, Homework Help, Discussion**