For each linear operator T, find a basis for each generalized eigenspace of T consisting

Chapter 7, Problem 3

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For each linear operator T, find a basis for each generalized eigenspace of T consisting of a union of disjoint cycles of generalized eigenvectors. Then find a Jordan canonical form J of T. (a) T is the linear operator on P2(R) defined by T(/(x)) = 2/(x) (b) V is the real vector space of functions spanned by the set of real valued functions {l,t, t2 ,e 1 , te1 }, and T is the linear operator on V defined by T(/) = /' . (c) T is the linear operator on M2x2 (#) defined by T(A) = I ) -A for all A G M2X2(#). (d) T(A) = 2A + At for all A G M2x2(i2)

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