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The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 8, 12, 15, and 18. The vector x1 is an eigenvector of A with eigenvalue 3, the vector æ2 is an eigenvector of A with eigenvalue 8, the vector x3 is an eigenvector of A with eigenvalue 12, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector az is an eigenvector of A with eigenvalue 18. Compute the dot products of the eigenvectors a; with each other. x1• x2 = x1· x3 = x1• x4 = x1. x5 = x2· x3 = x2· x4 = x2· x5 = x3· x4 = x3· X5 = x4 • x5 =

The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 8, 12, 15, and 18. The vector x1 is an eigenvector of A with eigenvalue 3, the vector æ2 is an eigenvector of A with eigenvalue 8, the vector x3 is an eigenvector of A with eigenvalue 12, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector az is an eigenvector of A with eigenvalue 18. Compute the dot products of the eigenvectors a; with each other. x1• x2 = x1· x3 = x1• x4 = x1. x5 = x2· x3 = x2· x4 = x2· x5 = x3· x4 = x3· X5 = x4 • x5 =

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 3, 8, 12, 15, and 18. The vector a1 is an eigenvector of A with eigenvalue 3, the vector x2 is an eigenvector of A with eigenvalue 8, the vector x3 is an eigenvector of A with eigenvalue 12, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector æz is an eigenvector of A with eigenvalue 18. Compute 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 3, 8, 12, 15, and 18. The vector a1 is an eigenvector of A with eigenvalue 3, the vector x2 is an eigenvector of A with eigenvalue 8, the vector x3 is an eigenvector of A with eigenvalue 12, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector æz is an eigenvector of A with eigenvalue 18. Compute 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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