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
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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.
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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