(Solution) - Let V be the space spanned by f1 sin -(2025 Original AI-Free Solution)

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Let V be the space spanned by f1 = sin x and f2 = cos ?-
(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 B?
(d) Compute the coordinate vector [h]B, where h = 2 sin x - 5 cos ?, and use 9 to obtain [h]