The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 7, 10, 15, and 21. The vector xị is an eigenvector of Awith eigenvalue 3, the vector x2 is an eigenvector ofeigenvalue 10, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector x; is an eigenvector of A witheigenvalue 21.with eigenvalue 7, the vector x3 is an eigenvector of A withCompute the dot products of the eigenvectors a; with each other.21. x2 =I1. X3 =X1. 24 =x2 · X3 =I2 · X4 =X2 · X5 =13 · X4 =13 · X5 =X4: x5 =

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The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3,7, 10, 15, and 21. The vector æ1 is an eigenvector of A with eigenvalue 3, the vector x, is an eigenvector of A with eigenvalue 7, the vector a3 is an eigenvector of A with eigenvalue 10, the vector 24 is an eigenvector of A with eigenvalue 15, and the vector æ; is an eigenvector of A with eigenvalue 21. Compute the dot products of the eigenvectors a with each other. x1. x2 = x1• 23 = x1. X4 = 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 3,7, 10, 15, and 21. The vector æ1 is an eigenvector of A with eigenvalue 3, the vector x, is an eigenvector of A with eigenvalue 7, the vector a3 is an eigenvector of A with eigenvalue 10, the vector 24 is an eigenvector of A with eigenvalue 15, and the vector æ; is an eigenvector of A with eigenvalue 21. Compute the dot products of the eigenvectors a with each other. x1. x2 = x1• 23 = x1. X4 = x2· X3 = x2 · X4 = X2 · X5 = X3 · X4 = x3 · X5 = X4 . X5 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The matrix A is a real symmetric 5 x 5 matrix with eigenvalues 3, 7, 10, 15, and 21. The vector xị is an eigenvector of A
with eigenvalue 3, the vector x2 is an eigenvector of
eigenvalue 10, the vector x4 is an eigenvector of A with eigenvalue 15, and the vector x; is an eigenvector of A with
eigenvalue 21.
with eigenvalue 7, the vector x3 is an eigenvector of A with
Compute the dot products of the eigenvectors a; with each other.
21. x2 =
I1. X3 =
X1. 24 =
x2 · X3 =
I2 · X4 =
X2 · X5 =
13 · X4 =
13 · X5 =
X4: x5 =

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