Assume that T is linear transformation. Find the matrix of T. a) T : R² → R² first rotates points through – * radians (clockwise) and then reflects points - through the horizontal x1 -axis. b)T : R2 → R² first reflects points through the horizontal x1-axis and then reflects points through the line x1 = x2. Show that this transformation is merely a rotation about the origin. What is the angle of the rotation?
Assume that T is linear transformation. Find the matrix of T. a) T : R² → R² first rotates points through – * radians (clockwise) and then reflects points - through the horizontal x1 -axis. b)T : R2 → R² first reflects points through the horizontal x1-axis and then reflects points through the line x1 = x2. Show that this transformation is merely a rotation about the origin. What is the angle of the rotation?
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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Linear Tranformation problem
Transcribed Image Text:Assume that T is linear transformation. Find the matrix of T.
a) T : R²
R? first rotates points through -* radians (clockwise) and then reflects points
through the horizontal x1 -axis.
b) T : R?
the line x1 = x2. Show that this transformation is merely a rotation about the origin. What is the
angle of the rotation?
· R² first reflects points through the horizontal x1 -axis and then reflects points through
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