(Linear Algebra) For each linear operator T on V, find the eigenvalues of T an an ordered basis B for V such that [T](sub)B is a diagonal matrix.V = P(sub)2(R) and T(f(x)) = xf'(x) + f(2)x + f(3)I'm just stuck on the problem and need a work through. Spent far too long on it.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
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(Linear Algebra) For each linear operator T on V, find the eigenvalues of T an an ordered basis B for V such that [T](sub)B is a diagonal matrix.
V = P(sub)2(R) and T(f(x)) = xf'(x) + f(2)x + f(3)

I'm just stuck on the problem and need a work through. Spent far too long on it.

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