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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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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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.
Transcribed Image Text: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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