Check the true statements below: U A. If Ax = Ar for some vector x, then 2 is an eigenvalue of A. B. To find the eigenvalues of A, reduce A to echelon form. O c.A number c is an eigenvalue of A if and only if the equation (A – cl)x = 0 has a nontrivial solution x. D. A matrix A is not invertible if and only if 0 is an eigenvalue of A. E. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A is an n X n matrix.
Check the true statements below:
U A. If Ax = Ax for some vector x, then 2 is an eigenvalue of A.
U 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 – cl)x = 0 has a nontrivial solution x.
O D. A matrix A is not invertible if and only if 0 is an eigenvalue of A.
U E. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
Transcribed Image Text:A is an n X n matrix. Check the true statements below: U A. If Ax = Ax for some vector x, then 2 is an eigenvalue of A. U 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 – cl)x = 0 has a nontrivial solution x. O D. A matrix A is not invertible if and only if 0 is an eigenvalue of A. U E. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
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