Show that the map below is linear transformation. Prove or disprove whether the map is injective and surjective A map T: V W is a linear map if the following two conditions are satisfied: (i) TX + Y Show that the map below is linear transformation. Prove or disprove whether the map is iniective and suriective A map T: V -> W is a linear map if the following two conditions are satisfied: (i) T(X + Y) = T(X) + T(Y) for any X, Y ? V, (ii)T(AX) = AT(X) for any X ? V and A? Reals

If Rx is the vector space of all polynomials, define T : Rx -> R by n n T arrk ak . k=0