Suppose that V is a vector space over R (not necessarily finite dimensional), and
that T1 : V −→ V and T2 : V −→ V are linear transformations from V to V with the
property that T3 = T2 ◦ T1 is the identity transformation, i.e. that T3(v) = v for all
vectors v in V.
T1(x1, x2, x3, . . .) = (0, x1, x2, x3, . . .)
T2(x1, x2, x3, x4, . . .) = (x2, x3, x4, . . .)
Show that T1 is not surjective
Show that T2 is not injective and find it's kernel

Question

Suppose that V is a vector space over R (not necessarily finite dimensional), and
that T1 : V −→ V and T2 : V −→ V are linear transformations from V to V with the
property that T3 = T2 ◦ T1 is the identity transformation, i.e. that T3(v) = v for all
vectors v in V.
T1(x1, x2, x3, . . .) = (0, x1, x2, x3, . . .)
T2(x1, x2, x3, x4, . . .) = (x2, x3, x4, . . .)
Show that T1 is not surjective
Show that T2 is not injective and find it's kernel