10. An n x n matrix is called nilpotent if for some positive integer k it follows A = 0 (the zero matrix). If A is a nilpotent matrix and k is the smallest possible integer such that A = 0, what are the possible values of det(A)? Justify your answer.

10. An n x n matrix is called nilpotent if for some positive integer k it follows A = 0 (the zero matrix). If A is a nilpotent matrix and k is the smallest possible integer such that A = 0, what are the possible values of det(A)? Justify your answer.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.4: Transistion Matrices And Similarity

Problem 29E

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10. An n x n matrix is called nilpotent if for some positive integer k it follows A = 0 (the zero matrix).
If A is a nilpotent matrix and k is the smallest possible integer such that A = 0, what are the possible
values of det(A)? Justify your answer.

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