Let V be the space spanned by f1 = sin x and f2 = cos - (a)

Question:

Let V be the space spanned by f1 = sin x and f2 = cos π-
(a) Show that gl = 2 sin x + cos x and g2 = 3 cos x form a basis for V.
(b) Find the transition matrix from B' = {g1, g2) to B = (f1, f2}.
(c) Find the transition matrix from B to Bʹ
(d) Compute the coordinate vector [h]B, where h = 2 sin x - 5 cos π, and use 9 to obtain [h]