4. Suppose that , and are distinct eigenvalues of matrix A with corresponding respectively. Show that x and y are linearly independent. eigenvectors x and y,

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
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Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
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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 λ and u are distinct eigenvalues of matrix A, let x be a right eigenvector for A,
and let y be a left eigenvector for u. Show that x and y are orthogonal.
Transcribed Image Text: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 λ and u are distinct eigenvalues of matrix A, let x be a right eigenvector for A, and let y be a left eigenvector for u. Show that x and y are orthogonal.
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