5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) =...

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Question

5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard

Find [T]b, the matrix for T relative to B.

Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.

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