A is an n x n matrix. Check the true statements below: A. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution .. B. To find the eigenvalues of A, reduce chelon form. C. If Ax = Xx for some vector, then A is an eigenvalue of A. D. Finding an eigenvector of A might be difficult, but checking wheth given vector is in fact an eigenvector is easy. E. 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: A. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution .. B. To find the eigenvalues of A, reduce chelon form. C. If Ax = Xx for some vector, then A is an eigenvalue of A. D. Finding an eigenvector of A might be difficult, but checking wheth given vector is in fact an eigenvector is easy. E. A matrix A is not invertible if and only if 0 is an eigenvalue of A.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
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