Hey all, We have not covered quotient vector spaces in class, but my homework (due before next lecture) covers a few proofs regarding quotient spaces. I've done some reading on them and some of their aspects, but as it is still a new concept, I am struggling with how to go about this proof. 1. The problem statement, all variables and given/known data Let [itex]M,N\subset L[/itex] where [itex]L[/itex] is a vector space and [itex]M,N[/itex] are linear subspaces of [itex]L[/itex]. Prove that the following mapping is a linear isomorphism: [tex](M+N)/N \rightarrow M/M \cap N[/tex] 2. The attempt at a solution Well, I understand that the general approach to proving this would be to show that the morphism is bijective. Thus, I want to show that whatever is in the codomain is in the domain such that it gets mapped to the codomain. I also want to show that uniqueness in the codomain implies uniqueness in the domain. Can someone give me some tips as to how to work with quotient spaces such that I can relate these to more elementary linear algebra problems? Hope that all makes sense. Thanks!