(Solution Download) If X is any set of vectors in an inner

If X is any set of vectors in an inner product space V, define
X? = {v | v in V, (v, x) = 0 for all x in X}.
(a) Show that X? is a subspace of V.
(b) If U = span, (u1,u2..., um}, show that (U? = {u1,...,um.
(c) If X? Y, show that Y? ? X?.
(d) Show that X? ? Y? = (X ? Y) ?