A square matrix A is called nilpotent if Ak = O for some k 1. (a)
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(a) Prove that the only eigenvalue of a nilpotent matrix is 0. (The converse is also true; see Exercise 8.6.18.)
(b) Find examples where Ak-1 ≠ O but Ak = O when k = 2, 3, and in general.
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a If Av v then 0 A k v k v and hence k 0 s...View the full answer
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