Question: Define T : R 3 R 3 by T(p) = p(0) + p(2)t - p(0)t 2 - p(2)t 3 . a. Find T(p) when

Define T :  R3 → R3 by T(p) = p(0) + p(2)t - p(0)t2 - p(2)t3. 

a. Find T(p) when p(t) = 1 - t2. Is p an eigenvector of T? If p is an eigenvector, what is its eigenvalue? 

b. Find T(p) when p(t) = t - t3. Is p an eigenvector of T? If p is an eigenvector, what is its eigenvalue?

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