(3) The double dual space of V, denoted V", is defined to be the dual space of V'. (In other words, V" = (V')'.) Define

F:V---->V", (Fv)(chi) = chi(v),for v belongs to V and chi belongs to V'.

(a) Show that F is a linear map.

(b) Show that if T: V--->V is linear, than T" o F = FoT, whereT" = (T')'.

(c) Show that if V is finite dimensional, then F is an isomorphism.