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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. OD. 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)¤ = 0 has a nontrivial solution i. OG. If A = li for some vector a, then A is an eigenvalue of A. OH. If A = X£ for some vector a, then i is an eigenvector of A. OI. 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. OD. 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)¤ = 0 has a nontrivial solution i. OG. If A = li for some vector a, then A is an eigenvalue of A. OH. If A = X£ for some vector a, then i is an eigenvector of A. OI. The eigenvalues of a matrix are on its main diagonal.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 38E
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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 (cl – A)a = 0 has a nontrivial solution i. G. If Az = A for some vector ä, then A is an eigenvalue of A. H. If Az |I. The eigenvalues of a matrix are on its main diagonal. Aã for some vector a, then i is an eigenvector of A.
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 (cl – A)a = 0 has a nontrivial solution i. G. If Az = A for some vector ä, then A is an eigenvalue of A. H. If Az |I. The eigenvalues of a matrix are on its main diagonal. Aã for some vector a, then i is an eigenvector of A.
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