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IX A IS PA(A) = X²(A – 4)(A – 2)°(A + 4)(A + 1)³(A² + 3). (a) (2 points) What is the size of A? (b) (3 points) What are the eigenvalues of A? What are the multiplicities of these eigenvalues as roots of pa(A)? (c) (3 points) Is A diagonalizable? Explain why or why not. (d) (2 points) True or False: Nul A = {0}.

IX A IS PA(A) = X²(A – 4)(A – 2)°(A + 4)(A + 1)³(A² + 3). (a) (2 points) What is the size of A? (b) (3 points) What are the eigenvalues of A? What are the multiplicities of these eigenvalues as roots of pa(A)? (c) (3 points) Is A diagonalizable? Explain why or why not. (d) (2 points) True or False: Nul A = {0}.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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2. Suppose that the characteristic polynomial of some n x n matrix A is given by PA(A) = X²(A – 4)(A – 2)*(A + 4)(A + 1)*(A² + 3). (a) (2 points) What is the size of A? (b) (3 points) What are the eigenvalues of A? What are the multiplicities of these eigenvalues as roots of pa(A)? (c) (3 points) Is A diagonalizable? Explain why or why not. (d) (2 points) True or False: Nul A = {0}.
Transcribed Image Text:2. Suppose that the characteristic polynomial of some n x n matrix A is given by PA(A) = X²(A – 4)(A – 2)*(A + 4)(A + 1)*(A² + 3). (a) (2 points) What is the size of A? (b) (3 points) What are the eigenvalues of A? What are the multiplicities of these eigenvalues as roots of pa(A)? (c) (3 points) Is A diagonalizable? Explain why or why not. (d) (2 points) True or False: Nul A = {0}.
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