2 1 -2 Consider the matrix A =0 0 0 0 -2 (a) What are the eigenvalues of A? smallest eigenvalue = middle eigenvalue = largest eigenvalue =| (b) Complete the following list of eigenvectors: an eigenvector for the smallest eigenvalue = an eigenvector for the middle eigenvalue = an eigenvector for the largest eigenvalue = (c) Give an invertible matrix P and a diagonal matrix D which satisfy P-AP =D: 9. P = and D = 1.
2 1 -2 Consider the matrix A =0 0 0 0 -2 (a) What are the eigenvalues of A? smallest eigenvalue = middle eigenvalue = largest eigenvalue =| (b) Complete the following list of eigenvectors: an eigenvector for the smallest eigenvalue = an eigenvector for the middle eigenvalue = an eigenvector for the largest eigenvalue = (c) Give an invertible matrix P and a diagonal matrix D which satisfy P-AP =D: 9. P = and D = 1.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:2 1 -2
Consider the matrix A =0 o
Lo o -2
(a) What are the eigenvalues of A?
smallest eigenvalue =
middle eigenvalue =
largest eigenvalue =
(b) Complete the following list of eigenvectors:
an eigenvector for the smallest eigenvalue =
1
an eigenvector for the middle eigenvalue =
an eigenvector for the largest eigenvalue =
(c) Give an invertible matrix P and a diagonal matrix D which satisfy P-AP =D:
1
1.
9
P =
and
D =
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