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Suppose that A and B are n x n matrices. Which of the following statements is(are) correct? Statements b and d a)lf 0 is an eigenvalue of A, then A is invertible b)The zero vector is in the eigenspace of A associated with an eigenvalue Statements a, b and d c)The matrix A and its transpose AT have different sets of eigenvalues. O d)lf 4 is an eigenvalue of A, then A - 4I is not invertible Statements b, c and d

Suppose that A and B are n x n matrices. Which of the following statements is(are) correct? Statements b and d a)lf 0 is an eigenvalue of A, then A is invertible b)The zero vector is in the eigenspace of A associated with an eigenvalue Statements a, b and d c)The matrix A and its transpose AT have different sets of eigenvalues. O d)lf 4 is an eigenvalue of A, then A - 4I is not invertible Statements b, c and d

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
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Suppose that A and B are n x n matrices. Which of the following statements is(are) correct? Statements b and d a)lf 0 is an eigenvalue of A, then A is invertible O b)The zero vector is in the eigenspace of A associated with an eigenvalue > O Statements a, b and d O c)The matrix A and its transpose AT have different sets of eigenvalues. d)lf 4 is an eigenvalue of A, then A - 4I is not invertible O Statements b, c and d A Previous Quiz
Transcribed Image Text:Suppose that A and B are n x n matrices. Which of the following statements is(are) correct? Statements b and d a)lf 0 is an eigenvalue of A, then A is invertible O b)The zero vector is in the eigenspace of A associated with an eigenvalue > O Statements a, b and d O c)The matrix A and its transpose AT have different sets of eigenvalues. d)lf 4 is an eigenvalue of A, then A - 4I is not invertible O Statements b, c and d A Previous Quiz
Suppose that A and B are n x n matrices. Which of the following statements is (are) false? O d) The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue n a)lf A-7 is a factor of the characteristic of A, then 7 is an eigenvalue of A Statements b, d and e O Statements b, c and e O Statements a, b and e O Statements b and e O e) If two matrices have the same set of eigenvalues, then they are similar O c)The eigenvalue of the n x n identity matrix is 1 with algebraic multiplicity n O b)A matrix A can have more than n eigenvalues Quiz saved at 1:00
Transcribed Image Text:Suppose that A and B are n x n matrices. Which of the following statements is (are) false? O d) The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue n a)lf A-7 is a factor of the characteristic of A, then 7 is an eigenvalue of A Statements b, d and e O Statements b, c and e O Statements a, b and e O Statements b and e O e) If two matrices have the same set of eigenvalues, then they are similar O c)The eigenvalue of the n x n identity matrix is 1 with algebraic multiplicity n O b)A matrix A can have more than n eigenvalues Quiz saved at 1:00
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