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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A is an n x n matrix. Check the true statements below: A. If Ax = λx for some vector x, then λ is an eigenvalue of A. B. A matrix A is not invertible if and only if 0 is an eigenvalue of A. C. A number c is an eigenvalue of A if and only if the equation (A - cI)x = 0 has a nontrivial solution x. D. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. E. To find the eigenvalues of A, reduce A to echelon form.
Transcribed Image Text:A is an n x n matrix. Check the true statements below: A. If Ax = λx for some vector x, then λ is an eigenvalue of A. B. A matrix A is not invertible if and only if 0 is an eigenvalue of A. C. A number c is an eigenvalue of A if and only if the equation (A - cI)x = 0 has a nontrivial solution x. D. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. E. To find the eigenvalues of A, reduce A to echelon form.
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