2. Let p1(t) = 1, p2(t) = 2t, p3(t) = -2+ 4t2 and p4(t) = -12t + 8t3 be polynomials is P3 (these are the first four Hermite polynomials). Consider the set B = {p1(t), p2(t), p3(t), p4(t)}. (a) Show that B is a basis for P3. (b) Determine the B-coordinate of the polynomial g(t) = 1+ 4t + 7t2.

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