Question: Please show all work necessary Define the operator T : P(R) - P(R) by T(p) = p', the derivative map. (a) Consider Pn(R), the vector

Please show all work necessary

Define the operator T : P(R) - P(R) by T(p) = p', the derivative map. (a) Consider Pn(R), the vector space of all polynomials of degree n or less. Is Pn (R) an invariant subspace of P(R) under 7? Why or why not? b) Find all eigenvalues and eigenvectors of T

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