Question: Consider the question in the image given. 2. Consider the linear transformation ap : 1% :~ R3 p(1)p'(1) p H 19(0) 16(0) - 10(1) all)

Consider the question in the image given.

2. Consider the linear transformation ap : \"1% :~ R3 p(1)p'(1) p H 19(0) 16(0) - 10(1) all) You may use the fact that 3 2 1 Mass: 0 1 1 a 1 0 1 where B = {122,33, 1} and 8 = {91,32,123}, the standard basis of R3. (a) Show that ap is invertible, and nd the polynomial (p1(a1,a2,a3) for a given vector ((11,012, (13) E R3. (b) Find the polynomial p E \"P2 such that p(1) = p'{1), p(1) = p'(1), and 39(0) = 19"(0) 1

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