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a) Define a linear operator on R by performing the following operations in order: i) a shear in the y-direction by a factor of 2, ii) a reflection in the x-axis, and, iii) 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.

a) Define a linear operator on R by performing the following operations in order: i) a shear in the y-direction by a factor of 2, ii) a reflection in the x-axis, and, iii) 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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a) Define a linear operator on R2 by performing the following operations in order: i) a shear in the y-direction by a factor of 2, ii) a reflection in the x-axis, and, iii) a compression in the y-direction by a factor of - 2 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. b) Consider the linear operator on R defined by performing the following operations in order: an expansion in the z-direction by a factor of 2, ii) a reflection in the x – z plane, and, iii) a rotation about the y-axis by an angle of t/3. Calculate the standard matrix of this linear transformation.
Transcribed Image Text:a) Define a linear operator on R2 by performing the following operations in order: i) a shear in the y-direction by a factor of 2, ii) a reflection in the x-axis, and, iii) a compression in the y-direction by a factor of - 2 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. b) Consider the linear operator on R defined by performing the following operations in order: an expansion in the z-direction by a factor of 2, ii) a reflection in the x – z plane, and, iii) a rotation about the y-axis by an angle of t/3. Calculate the standard matrix of this linear transformation.
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