Problem 3. (20-10-10 points) Let P, be the vector space of polynomials of degree no more than n. Define the linear trans

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Problem 3 20 10 10 Points Let P Be The Vector Space Of Polynomials Of Degree No More Than N Define The Linear Trans 1 (351.1 KiB) Viewed 17 times

Problem 3. (20-10-10 points) Let P, be the vector space of polynomials of degree no more than n. Define the linear transformation Ton P2 by T(p(t)) = p'(t) (t+1) I where p'(t) is the derivative of p(t) (you are given the fact that this is a linear transformation on P₂). (1) Let B = {1, t, tº be the standard basis of P₂. Compute [7]B, the matrix for T relative to B. (2) Show that 2 is an eigenvalue of T, and find a corresponding eigenvector.