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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. The eigenvalues of a matrix are on its main diagonal. B. A number c is an eigenvalue of A if and only if the equation (cI - A) x = 0 has a nontrivial solution x. ☐ C. An eigenspace of A is just a kernel of a certain matrix. ☐ D. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. E. If Ax = Xx for some vector x, then A is an eigenvalue of A. F. If +5 is a factor of the characteristic polynomial of A, then -5 is an eigenvalue of A. ☐ G. If Ax = Xx for some vector x, then x is an eigenvector of A. ☐ H. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. I. A matrix A is not invertible if and only if 0 is an eigenvalue of A.

A is an n x n matrix. Check the true statements below. Note you only have 5 attempts for this question. A. The eigenvalues of a matrix are on its main diagonal. B. A number c is an eigenvalue of A if and only if the equation (cI - A) x = 0 has a nontrivial solution x. ☐ C. An eigenspace of A is just a kernel of a certain matrix. ☐ D. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. E. If Ax = Xx for some vector x, then A is an eigenvalue of A. F. If +5 is a factor of the characteristic polynomial of A, then -5 is an eigenvalue of A. ☐ G. If Ax = Xx for some vector x, then x is an eigenvector of A. ☐ H. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. I. A matrix A is not invertible if and only if 0 is an eigenvalue of A.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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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. The eigenvalues of a matrix are on its main diagonal. B. A number c is an eigenvalue of A if and only if the equation (cI - A) x = 0 has a nontrivial solution x. ☐ C. An eigenspace of A is just a kernel of a certain matrix. ☐ D. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. E. If Ax = Xx for some vector x, then A is an eigenvalue of A. F. If +5 is a factor of the characteristic polynomial of A, then -5 is an eigenvalue of A. ☐ G. If Ax = Xx for some vector x, then x is an eigenvector of A. ☐ H. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. I. A matrix A is not invertible if and only if 0 is an eigenvalue 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. The eigenvalues of a matrix are on its main diagonal. B. A number c is an eigenvalue of A if and only if the equation (cI - A) x = 0 has a nontrivial solution x. ☐ C. An eigenspace of A is just a kernel of a certain matrix. ☐ D. If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues. E. If Ax = Xx for some vector x, then A is an eigenvalue of A. F. If +5 is a factor of the characteristic polynomial of A, then -5 is an eigenvalue of A. ☐ G. If Ax = Xx for some vector x, then x is an eigenvector of A. ☐ H. If one multiple of one row of A is added to another row, the eigenvalues of A do not change. I. A matrix A is not invertible if and only if 0 is an eigenvalue of A.
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