1. The problem statement, all variables and given/known data Prove that dim null T∗ = dim null T + dimW − dimV and dim range T∗ = dim range T for every T ∈ L(V,W). 2. Relevant equations 3. The attempt at a solution I have my solution written down, but just to make sure... I think that nullT*=0 since W is a subspace of V and mapping from W to V with T* yields the same result as mapping from W to W since W is in V, so it would only make sense that T(wi) is in V and no vector (besides 0) is in nullT*. Just want to make sure my reasoning here is right. This isn't my solution, btw, but a crucial finding.