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)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 41EQ
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