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Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

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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10/12 1a and 1b, Part of the same questions.
Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees. Check Answer
Transcribed Image Text:Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 7 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 5 in the y-direction. 4. Rotate counter-clockwise by 90 degrees. Check Answer
Find the standard matrix for the linear transformation T: R² → R² that shears vertically, with 1 1 T([J]) = [-3.7] ² and then reflects points about the origin. Check Answer
Transcribed Image Text:Find the standard matrix for the linear transformation T: R² → R² that shears vertically, with 1 1 T([J]) = [-3.7] ² and then reflects points about the origin. Check Answer
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