Guided Proof Prove that nonzero nilpotent matricesare not diagonalizable.Getting
Chapter 7, Problem 7.125(choose chapter or problem)
Guided Proof Prove that nonzero nilpotent matricesare not diagonalizable.Getting Started: From Exercise 78 in Section 7.1, youknow that 0 is the only eigenvalue of the nilpotentmatrix Show that it is impossible for to bediagonalizable.(i) Assume is diagonalizable, so there exists aninvertible matrix such that whereis the zero matrix.(ii) Find in terms of and(iii) Find a contradiction and conclude that nonzeronilpotent matrices are not diagonalizable
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