? ? ? 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 ʼn distinct eigenvalues. 3. If A is invertible, then A is diagonalizable.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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