Let V be a finite-dimensional vectorspace over a field F, and letT:V → V be a lineartransformation whose fifth powerT5 is the identity.(a) Show that T is alwaysdiagonalisable if F is the field ofcomplex numbers.(b) If F is the field of real numbers,show that T is only diagonalisableif it is equal to the identity.

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Answered: Let V be a finite-dimensional vector…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 2TFE

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