Recent content by pte419

Thanks guys, I've got one more question. I did: dim(V+U3) and I've ended up with: dim(V+U3) = dimU1 + dimU2 - dim(U1∩U2) + dimU3 - dim(V∩U3) Is there a property I can use to show that dim(V∩U3) is equivalent to the terms I still need to include for the proof? I can't find anything...

proof I am only asked to prove equation one, but in doing that, I am allowed to use equation 2.

Suppose S, T \in L(V) are such that ST=TS. Prove that null(T-\lambdaI) is invariant under S for every \lambda \in F. I can't find anything helpful in my book, I'm not sure where to start...

[b]1. For subsets U1, U2, U3 of a finite set, prove that dim(U1+U2+U3) = dimU1 + dimU2 + dimU3 - dim(U1∩U2) - dim(U1∩U3) - dim(U2∩U3) + dim(U1∩U2∩U3) [b]2. dim(U1+U2) = dimU1 + dimU2 - dim(U1∩U2) [b]3. I found that U1+U2 theorem in my book, and I think I should use that, but...