Let T1: P2 P3 and T2: P3 P3 be the linear transformations given by the formulas T1 p(x)

Chapter 8, Problem 23

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Let T1: P2 P3 and T2: P3 P3 be the linear transformations given by the formulas T1 p(x) = xp(x) and T2 p(x) = p(x + 1) (a) Find formulas for T 1 1 p(x) , T 1 2 p(x) , and (T 1 1 T 1 2 ) p(x) . (b) Verify that (T2 T1)1 = T 1 1 T 1 2 .

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