Hey people. I find myself getting through my course but currently with not as much understanding as I would like. We've got to some proofs and i either vaguely understand them or do not know how to prove them. 1. The problem statement, all variables and given/known data The first would be to prove the Dimension theorem that. dimU + dimV = dim(U + V) + dim( U intersection V ) The second is if U,V are finite dimensional vector spaces over a field, and T: V -> W is a bijection Show dimU = dimW The last is to do with the Rank-Nullity Theorem and a basic linear transformation T: Rn -> Rm That if m < n prove that T is not injective And if m = n prove that T is injective iff T is surjective. Some general insight into these proofs would be very very helpful. All feedback would be very much appreciated. Thanks.