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? ? 4. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. 5. The eigenvalues of a matrix are the entries on its main diagonal.

? ? 4. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. 5. The eigenvalues of a matrix are the entries on its main diagonal.

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? 1. The sum of two eigenvectors of a matrix is always an eigenvector. 2. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. 3. If A is invertible, then A is diagonalizable. 4. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. 5. The eigenvalues of a matrix are the entries on its main diagonal.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false for a square matrix A? 1. The sum of two eigenvectors of a matrix is always an eigenvector. 2. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. 3. If A is invertible, then A is diagonalizable. 4. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. 5. The eigenvalues of a matrix are the entries on its main diagonal.
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