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The matrix A is a real symmetric 5 × 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector æ1 is an eigenvector of A with eigenvalue 2, the vector x2 is an eigenvector of A with eigenvalue 6, the vector æ3 is an eigenvector of A with eigenvalue 11, the vector æ4 is an eigenvector of A with eigenvalue 14, and the vector æz is an eigenvector of A with eigenvalue 19. Compute the dot products of the eigenvectors a; with each other. 21• x2 = 21. 25 = x2· x3 = x2· x4 = x2· 25 = x3. X4 = 23· 25 =

The matrix A is a real symmetric 5 × 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector æ1 is an eigenvector of A with eigenvalue 2, the vector x2 is an eigenvector of A with eigenvalue 6, the vector æ3 is an eigenvector of A with eigenvalue 11, the vector æ4 is an eigenvector of A with eigenvalue 14, and the vector æz is an eigenvector of A with eigenvalue 19. Compute the dot products of the eigenvectors a; with each other. 21• x2 = 21. 25 = x2· x3 = x2· x4 = x2· 25 = x3. X4 = 23· 25 =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 24EQ
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The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector x1 is an eigenvector of A with eigenvalue 2, the vector x2 is an eigenvector of A with eigenvalue 14, and the of A with eigenvalue 6, the vector x3 is an eigenvector of A with eigenvalue 11, the vector x4 is an eigenvector vector x, is an eigenvector of A with eigenvalue 19. the dot products of the eigenvectors x; with each other. X1 X2 X1• x3 = X1•X4 = X1• X5 X2· x3 = X2· X4 = X2· X5 = X3 • X4 = X3 · X5 = X4• X5 =
Transcribed Image Text:The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector x1 is an eigenvector of A with eigenvalue 2, the vector x2 is an eigenvector of A with eigenvalue 14, and the of A with eigenvalue 6, the vector x3 is an eigenvector of A with eigenvalue 11, the vector x4 is an eigenvector vector x, is an eigenvector of A with eigenvalue 19. the dot products of the eigenvectors x; with each other. X1 X2 X1• x3 = X1•X4 = X1• X5 X2· x3 = X2· X4 = X2· X5 = X3 • X4 = X3 · X5 = X4• X5 =
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