Question:
Suppose f and g are isomorphisms from U to V. Prove or disprove each of the following statements:
a) The mapping f + g is an isomorphism from U to V
I have no idea where to start. Do I need to show that f(u) + g(u) = (f+g)(u)? Do I need to show that (f+g) is 1-1 and onto?
that's not what you were supposed to show. and why are you choosing bases? I suppose this is a linear algebra problem as opposed to an abstract algebra problem(?) if so, then we would use the definition that an isomorphism between two vector spaces is a bijective linear transformation from one to the other. so, is it true that if we take two such transformations, their sum will be such a transformation?