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Problem 3 §7.2, Exercise 4. Consider the matrix -1 1 1 -1 1 -1 A = 1 (a) Verify that the characteristic polynomial of A is pa(A) = (X – 1)(A+2)². (b) Show that (1, 1, 1) is an eigenvector of A corresponding to A = 1. (c) Show that (1, 1, 1) is orthogonal to every eigenvector of A corresponding to the eigenvalue A= -2.

Problem 3 §7.2, Exercise 4. Consider the matrix -1 1 1 -1 1 -1 A = 1 (a) Verify that the characteristic polynomial of A is pa(A) = (X – 1)(A+2)². (b) Show that (1, 1, 1) is an eigenvector of A corresponding to A = 1. (c) Show that (1, 1, 1) is orthogonal to every eigenvector of A corresponding to the eigenvalue A= -2.

Advanced Engineering Mathematics
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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Please help. This problem involves characteristic polynomials and eigenvectors. Thank you.

Problem 3 §7.2, Exercise 4. Consider the matrix :) 1 1 A 1 -1 1 1 -1 (a) Verify that the characteristic polynomial of A is pa(A) = (A – 1)(A+2)². (b) Show that (1, 1, 1) is an eigenvector of A corresponding to1 = 1. (c) Show that (1,1, 1) is orthogonal to every eigenvector of A corresponding to the eigenvalue X = -2.
Transcribed Image Text:Problem 3 §7.2, Exercise 4. Consider the matrix :) 1 1 A 1 -1 1 1 -1 (a) Verify that the characteristic polynomial of A is pa(A) = (A – 1)(A+2)². (b) Show that (1, 1, 1) is an eigenvector of A corresponding to1 = 1. (c) Show that (1,1, 1) is orthogonal to every eigenvector of A corresponding to the eigenvalue X = -2.
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