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Problem 4. (a) Define a linear operator on R2 by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of . Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0,0), (0, 1), (1,0) and (1,1) under this linear map.

Problem 4. (a) Define a linear operator on R2 by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of . Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0,0), (0, 1), (1,0) and (1,1) under this linear map.

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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Problem 4. (a) Define a linear operator on R² by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of ;. Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0, 0), (0, 1), (1,0) and (1,1) under this linear map.
Transcribed Image Text:Problem 4. (a) Define a linear operator on R² by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of ;. Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0, 0), (0, 1), (1,0) and (1,1) under this linear map.
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