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? Are the following statements true or false for a square matrix A? 1. If Ax = λx for some vector x and some scalar λ, then x is an eigenvector of A.

? Are the following statements true or false for a square matrix A? 1. If Ax = λx for some vector x and some scalar λ, then x is an eigenvector of A.

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. If Ax = λx for some vector x and some scalar λ, then x is an eigenvector of A. ✓2. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. 3. If Ax = λx for some vector x and some scalar λ, then λ is an eigenvalue of A. 4. If A is invertible, then A is diagonalizable. 5. A matrix A is singular if and only if 0 is an eigenvalue of A.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false for a square matrix A? 1. If Ax = λx for some vector x and some scalar λ, then x is an eigenvector of A. ✓2. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. 3. If Ax = λx for some vector x and some scalar λ, then λ is an eigenvalue of A. 4. If A is invertible, then A is diagonalizable. 5. A matrix A is singular if and only if 0 is an eigenvalue of A.
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