A is an n x n matrix. Check the true statements below. Note you only have 5 attempts for this question. OA. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. OB. If A + 5 is a factor of the characteristic polynomial of A, then –5 is an eigenvalue of A. OC. A matrix A is not invertible if and only if 0 is an eigenvalue of A. D. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. OE. An eigenspace of A is just a kernel of a certain matrix. OF. A number c is an eigenvalue of A if and only if the equation (cI – A)ã = 0 has a nontrivial solution i. OG. If Ax = Xã for some vector a, then A is an eigenvalue of A. |H. If Aæ = Xã for some vector ã, then a is an eigenvector of A. O1. The eigenvalues of a matrix are on its main diagonal.
A is an n x n matrix. Check the true statements below. Note you only have 5 attempts for this question. OA. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. OB. If A + 5 is a factor of the characteristic polynomial of A, then –5 is an eigenvalue of A. OC. A matrix A is not invertible if and only if 0 is an eigenvalue of A. D. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. OE. An eigenspace of A is just a kernel of a certain matrix. OF. A number c is an eigenvalue of A if and only if the equation (cI – A)ã = 0 has a nontrivial solution i. OG. If Ax = Xã for some vector a, then A is an eigenvalue of A. |H. If Aæ = Xã for some vector ã, then a is an eigenvector of A. O1. The eigenvalues of a matrix are on its main diagonal.
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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Transcribed Image Text:A is an n x n matrix.
Check the true statements below. Note you only have 5 attempts for this question.
A. If vi and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.
|B. If A + 5 is a factor of the characteristic polynomial of A, then –5 is an eigenvalue of A.
C. A matrix A is not invertible if and only if 0 is an eigenvalue of A.
D. If one multiple of one row of A is added to another row, the eigenvalues of A do not change.
E. An eigenspace of A is just a kernel of a certain matrix.
F. A number c is an eigenvalue of A if and only if the equation (cI – A)z = 0 has a nontrivial solution a.
|G. If A = A for some vector i, then A is an eigenvalue of A.
OH. If Ax :
|I. The eigenvalues of a matrix are on its main diagonal.
Az for some vector i, then i is an eigenvector of A.
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