Let A be a square matrix. Which of the following statements are always true? i) if A is an eigenvalue for A, then -A is an eigenvalue for -A ii) if V is an eigenvector for A, then V is also an eigenvector for 2A iii) The eigenspace for the matrix A for the eigenvalue A has dimension equal to the multiplicity of A i) only ii) and iii) only i) and ii) only i) and iii) only 1), ii) and ili)

Let A be a square matrix. Which of the following statements are always true? i) if A is an eigenvalue for A, then -A is an eigenvalue for -A ii) if V is an eigenvector for A, then V is also an eigenvector for 2A iii) The eigenspace for the matrix A for the eigenvalue A has dimension equal to the multiplicity of A i) only ii) and iii) only i) and ii) only i) and iii) only 1), ii) and ili)

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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Question

Let A be a square matrix. Which of the following statements are always true?
i) if A is an eigenvalue for A, then -A is an eigenvalue for -A
ii) if V is an eigenvector for A, then V is also an eigenvector for 2A
iii) The eigenspace for the matrix A for the eigenvalue A has dimension equal to the multiplicity of A
i) only
ii) and iii) only
i) and ii) only
i) and iii) only
1), ii) and ili)

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