Pls helpLet T: V-> W be a linear map, and let x1,....,xm and y1,...yn be two lists of vector in V. Suppose that
(a) x1,...xm generate Ker T and
(b) T(y1),...,T(yn) genterate W.
Show that the list x1,....,xm, y1,...,yn generates V.
I'm working on this question as well. I thought the same but realized that it only proves some vectors in W can be generated by T(b_1*y_1 + ... + b_n*y_n). this is correct, right?
Do you have any hints? I'm pretty stuck but I've been working on it for a while.
EDIT> I was thinking of using dimV=dimT(v)+dim(KerT) (v in V), would this help at all?