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? if 0 is an eigenvalue of A. 4. A matrix A is singular if and only

? if 0 is an eigenvalue of A. 4. A matrix A is singular if and only

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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Problem 4. Are the following statements true or false for a square matrix A? ? 1. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors. ? reduce A to echelon form. 2. To find the eigenvalues of A, ? 3. The sum of two eigenvectors of a matrix is always an eigenvector. ? if 0 is an eigenvalue of A. 4. A matrix A is singular if and only ? 5. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
Transcribed Image Text:Problem 4. Are the following statements true or false for a square matrix A? ? 1. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors. ? reduce A to echelon form. 2. To find the eigenvalues of A, ? 3. The sum of two eigenvectors of a matrix is always an eigenvector. ? if 0 is an eigenvalue of A. 4. A matrix A is singular if and only ? 5. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
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