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19 20 -16 S = 20 13 4 4 31 For an invertible matrix A, it can be shown that A = QAQ-1, where A is the matrix containing the eigenvalues along the diagonal with zeros elsewhere and Q is a matrix containing the corresponding eigenvectors in the same order. This is known as eigendecomposition. b) Orthogonal matrices have a special property that QT = Q-1. Check if Q is rthogonal. c) Hence or otherwise find the solution to the linear system Sx = b, where b = (10,2,3)".

19 20 -16 S = 20 13 4 4 31 For an invertible matrix A, it can be shown that A = QAQ-1, where A is the matrix containing the eigenvalues along the diagonal with zeros elsewhere and Q is a matrix containing the corresponding eigenvectors in the same order. This is known as eigendecomposition. b) Orthogonal matrices have a special property that QT = Q-1. Check if Q is rthogonal. c) Hence or otherwise find the solution to the linear system Sx = b, where b = (10,2,3)".

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 32E
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3. a) Find the eigenvalues and eigenvectors for the following matrix: 19 20 -16) S = 20 13 4 -16 4 31 For an invertible matrix A, it can be shown that A = QAQ-1, where A is the matrix containing the eigenvalues along the diagonal with zeros elsewhere and Q is a matrix containing the corresponding eigenvectors in the same order. This is known as eigendecomposition. b) Orthogonal matrices have a special property that QT = Q-1. Check if Q is orthogonal. c) Hence or otherwise find the solution to the linear system Sx = b, where b = (10,2,3)".
Transcribed Image Text:3. a) Find the eigenvalues and eigenvectors for the following matrix: 19 20 -16) S = 20 13 4 -16 4 31 For an invertible matrix A, it can be shown that A = QAQ-1, where A is the matrix containing the eigenvalues along the diagonal with zeros elsewhere and Q is a matrix containing the corresponding eigenvectors in the same order. This is known as eigendecomposition. b) Orthogonal matrices have a special property that QT = Q-1. Check if Q is orthogonal. c) Hence or otherwise find the solution to the linear system Sx = b, where b = (10,2,3)".
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