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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
Related questions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe89a174f-7d5f-4dc6-a2a6-aa3a1285f66b%2F1220dd78-ee28-4c3a-866c-df40d23391a0%2Fkzns7qi_processed.jpeg&w=3840&q=75)
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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