Let A be a 2 x 2 matrix. Assume ₁ and ₂ are the two distinct non-zero eigenvalues of A. Determine whether the following statements are always true? If true, justify why. If not true, provide a couterexample. Statement A: If v₁ is an eigenvector corresponding to A₁ and 2 is an eigenvector corresponding to A₂, then v₁ + ₂ is an eigenvector of A, corresponding to eigenvalue A₁ + A₂. Statement B: If c ER, then cu₁ is an eigenvector of A, corresponding to A₁.

Let A be a 2 x 2 matrix. Assume ₁ and ₂ are the two distinct non-zero eigenvalues of A. Determine whether the following statements are always true? If true, justify why. If not true, provide a couterexample. Statement A: If v₁ is an eigenvector corresponding to A₁ and 2 is an eigenvector corresponding to A₂, then v₁ + ₂ is an eigenvector of A, corresponding to eigenvalue A₁ + A₂. Statement B: If c ER, then cu₁ is an eigenvector of A, corresponding to A₁.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 6EQ

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