29. Let the characteristic polynomial of a matrix be p(2)= 2² +62+9. a) What are the dimensions of the matrix? b) What is the determinant of the matrix? c) Suppose the matrix is invertible. What is the characteristic polynomial for the inverse matrix? d) What is the characteristic polynomial of the transpose of the matrix? Explain your reasoning.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
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29. Let the characteristic polynomial of a matrix be p(2)= 2² +62+9.
a) What are the dimensions of the matrix?
b) What is the determinant of the matrix?
c) Suppose the matrix is invertible. What is the characteristic polynomial for the inverse
matrix?
d) What is the characteristic polynomial of the transpose of the matrix? Explain your
reasoning.
Transcribed Image Text:29. Let the characteristic polynomial of a matrix be p(2)= 2² +62+9. a) What are the dimensions of the matrix? b) What is the determinant of the matrix? c) Suppose the matrix is invertible. What is the characteristic polynomial for the inverse matrix? d) What is the characteristic polynomial of the transpose of the matrix? Explain your reasoning.
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