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A. If Ax = xx for some vector x and some scalar A, then x is an eigenvector of A. B. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. C. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. D. To find the eigenvalues of A, reduce A to echelon form. E. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution X.

A. If Ax = xx for some vector x and some scalar A, then x is an eigenvector of A. B. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. C. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. D. To find the eigenvalues of A, reduce A to echelon form. E. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution X.

Advanced Engineering Mathematics
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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Are the following statements true or false for a square matrix A?

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A. If Ax = Xx for some vector x and some scalar X, then x is an eigenvector of A. B. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. C. If an n x n matrix A is diagonalizable, then A hasn distinct eigenvalues. D. To find the eigenvalues of A, reduce A to echelon form. E. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution X.
Transcribed Image Text:A. If Ax = Xx for some vector x and some scalar X, then x is an eigenvector of A. B. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. C. If an n x n matrix A is diagonalizable, then A hasn distinct eigenvalues. D. To find the eigenvalues of A, reduce A to echelon form. E. A number c is an eigenvalue of A if and only if the equation (A - cI)x= 0 has a nontrivial solution X.
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