Let T: R² R² be the linear map T(x, y) = (y,x). (a) What is the standard matrix of T? (b) Give a geometric description of T using the word reflection. (c) Find the eigenvalues of T (just using the definition).
Let T: R² R² be the linear map T(x, y) = (y,x). (a) What is the standard matrix of T? (b) Give a geometric description of T using the word reflection. (c) Find the eigenvalues of T (just using the definition).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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![Let T : R² → R² be the linear map T(x, y)
=
(y,x).
(a) What is the standard matrix of T?
(b) Give a geometric description of T using the word reflection.
(c) Find the eigenvalues of T (just using the definition).
(d) Find an eigenvector for each eigenvalue.
(e) For each of your eigenvectors v from (d), graph v and Tv = \v.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2Fb3baac91-e79a-4d27-8c4e-3a02049a32b7%2Fbzp5pr_processed.png&w=3840&q=75)
Transcribed Image Text:Let T : R² → R² be the linear map T(x, y)
=
(y,x).
(a) What is the standard matrix of T?
(b) Give a geometric description of T using the word reflection.
(c) Find the eigenvalues of T (just using the definition).
(d) Find an eigenvector for each eigenvalue.
(e) For each of your eigenvectors v from (d), graph v and Tv = \v.
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