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For each of the following transformations, determine T(₁) geometrically (meaning using the description, not by finding the matrix.) Is é an eigenvector? (Yes or No). If Yes, write the corresponding eigenvalue. Hint: the eigenvalue could possibly be 0. (a) T₁ reflection across the x-axis. (b) T2 vertical stretch by 2 (c) T3 = rotation by 90° counterclockwise.

For each of the following transformations, determine T(₁) geometrically (meaning using the description, not by finding the matrix.) Is é an eigenvector? (Yes or No). If Yes, write the corresponding eigenvalue. Hint: the eigenvalue could possibly be 0. (a) T₁ reflection across the x-axis. (b) T2 vertical stretch by 2 (c) T3 = rotation by 90° counterclockwise.

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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1. For each of the following transformations, determine T(₁) geometrically (meaning using the description, not by finding the matrix.) Is e an eigenvector? (Yes or No). If Yes, write the corresponding eigenvalue. Hint: the eigenvalue could possibly be 0. (a) T₁= reflection across the x-axis. (b) T2 vertical stretch by 2 (c) T3 = rotation by 90° counterclockwise. (d) T4 = rotation by 180° counterclockwise. (e) T5 (orthogonal) projection onto the y-axis.
Transcribed Image Text:1. For each of the following transformations, determine T(₁) geometrically (meaning using the description, not by finding the matrix.) Is e an eigenvector? (Yes or No). If Yes, write the corresponding eigenvalue. Hint: the eigenvalue could possibly be 0. (a) T₁= reflection across the x-axis. (b) T2 vertical stretch by 2 (c) T3 = rotation by 90° counterclockwise. (d) T4 = rotation by 180° counterclockwise. (e) T5 (orthogonal) projection onto the y-axis.
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