6. Let V be the vector space above. Consider the maps T : V → V
And S : V → V
defined by T(a1,a2,a3,...) = (a2,a3,a4,...) and S(a1,a2,a3,...)
= (0,a1,a2,...).
(a) [optional] Show that T and S are linear.
(b) Show that T is surjective but not injective.
(c) Show that S is injective but not surjective.
(d) Show that V = im(T) + ker(T) but im(T) ∩ ker(T) ̸= {0}.
(e) Show that im(S) ∩ ker(S) = {0}...