Question: Consider the subspace W of D, given by W = span (sin x, cos x). (a) Show that the differential operator D maps W into

Consider the subspace W of D, given by
W = span (sin x, cos x).
(a) Show that the differential operator D maps W into itself.
(b) Find the matrix of D with respect to
B = {sin x, cos x}.
(c) Compute the derivative of f(x) = 3 sin x - 5 cos x indirectly, using Theorem 6.26, and verify that it agrees with f'(x) as computed directly.

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