Let V be the space spanned by f1 = sin x and f2 = cos x. (a) Show that g1 = 2 sin x +

Chapter 4, Problem 5

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Let V be the space spanned by f1 = sin x and f2 = cos x. (a) Show that g1 = 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 x, and use (12) to obtain [h]B . (e) Check your work by computing [h]B directly.

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