Let \( A \) be an arbitrary \( n \times n \) matrix. Show that if \( \lambda_1 \) and \( \lambda_2 \) are two eigenvalues with \( \lambda_1 \neq \lambda_2 \) and eigenvectors \( \mathbf{v}_1 \) and \( \mathbf{v}_2 \), respectively, then \( \mathbf{v}_1 \) and \( \mathbf{v}_2 \) are linearly independent.

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Answered: Let A be a arbitrary n x n matrix, Show…

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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Let A be a arbitrary n x n matrix, Show that if A1 and A2 are two eigenvalues with A1 # 12 and eigenvectors vi and v2, respectively. Show that vị and v2 are linerly independent.