Check the true statements below: A. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. B. To find the eigenvalues of A, reduce A to echelon form. C. A number c is an eigenvalue of A if and only if the equation (A D. A matrix A is not invertible if and only if 0 is an eigenvalue of A. E. If Ax = 1x for some vector x, then 1 is an eigenvalue of A. cI)x = 0 has a nontrivial solution x.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 16EQ
Question

A is an n×n matrix. 

 

 

Check the true statements below:
A. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
B. To find the eigenvalues of A, reduce A to echelon form.
C. A number c is an eigenvalue of A if and only if the equation (A – cI)x
D. A matrix A is not invertible if and only if 0 is an eigenvalue of A.
E. If Ax = 1x for some vector x, then å is an eigenvalue of A.
O has a nontrivial solution x.
Transcribed Image Text:Check the true statements below: A. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. B. To find the eigenvalues of A, reduce A to echelon form. C. A number c is an eigenvalue of A if and only if the equation (A – cI)x D. A matrix A is not invertible if and only if 0 is an eigenvalue of A. E. If Ax = 1x for some vector x, then å is an eigenvalue of A. O has a nontrivial solution x.
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