Consider the linear transformation T : P2 ? P2 given by T(p(x))= p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x,x2} for P2.
(a) Find the matrix A for T with respect to the basis B.
(b) Find the eigenvalues of A, and a basis for R 3 consisting ofeigenvectors of A.
(c) Find a basis for P2 consisting of eigenvectors for T.
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