1. The problem statement, all variables and given/known data Let S : U →V and T : V →W be linear maps. Given that dim(U) = 2, dim(V ) = 1, and dim(W) = 2, could T composed of S be an isomorphism? 2. Relevant equations If Dim(v) > dim(W), then T is 1-1 If Dimv < dim(w), then T is not onto. 3. The attempt at a solution So this seems like a tricky question, but I am having trouble proving whether or not this is an isomorphism. While I know that T composed of S (u) = T(S(u)), S: U→V and T:V→W, this would be an isomorphism if dim(U) = Dim(W). But does the fact that S maps to V, which is one dimension less than U and W, affect that this is an isomorphism? I think an example could be helpful in helping me understand this problem. Thank you.