4. Suppose that and are distinct eigenvalues of matrix A with corresponding eigenvectors x and y, respectively. Show that x and y are linearly independent. 5. Let 2 and are distinct eigenvalues of matrix 1, let be a right cigsinvector

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 11AEXP
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4. Suppose that and λ, are distinct eigenvalues of matrix A with corresponding
eigenvectors x and y, respectively. Show that x and y are linearly independent.
5. Let A and are distinct eigenvalues of matrix , let a be a right cigonvector
and let p be a left eigenvector for 7. Show that x and y are orthogonal.
Transcribed Image Text:4. Suppose that and λ, are distinct eigenvalues of matrix A with corresponding eigenvectors x and y, respectively. Show that x and y are linearly independent. 5. Let A and are distinct eigenvalues of matrix , let a be a right cigonvector and let p be a left eigenvector for 7. Show that x and y are orthogonal.
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