4 Find a matrix for each transformation below, or explain why no such matrix exists. (b) R: R² → R2, where R is rotation clockwise by 135⁰. (d) P: R² → R2, where P is projection onto the y-axis. (e) F: R² R2, where F is reflection over the line y = x.

4 Find a matrix for each transformation below, or explain why no such matrix exists. (b) R: R² → R2, where R is rotation clockwise by 135⁰. (d) P: R² → R2, where P is projection onto the y-axis. (e) F: R² R2, where F is reflection over the line y = x.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 17CM

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Question

Please explain how to do question B, D, and E. I am not sure how to show rotation by a matrix transformation. Thank you for your help.

4 Find a matrix for each transformation below, or explain
why no such matrix exists.
(b) R : R² → R², where R is rotation clockwise by
135º.
(d) P: R² R2, where P is projection onto the y-axis.
(e) F: R² R2, where F is reflection over the line
→
y = x.

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