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(a) This question concerns transformations using matrix multiplication. (i) Formulate the matrix that will first rotate by t/3 radians, then scale by a factor of 2 in the x direction. (ii) Formulate the matrix that will first scale by a factor of 2 in the x direction, then rotate by 7/3 radians. (iii) By applying these transformation matrices to the unit square, show that the order of the transformations matter. Plot each transformed unit square. Note: the unit square has vertices (0,0), (1,0), (1,1) and (0,1).

(a) This question concerns transformations using matrix multiplication. (i) Formulate the matrix that will first rotate by t/3 radians, then scale by a factor of 2 in the x direction. (ii) Formulate the matrix that will first scale by a factor of 2 in the x direction, then rotate by 7/3 radians. (iii) By applying these transformation matrices to the unit square, show that the order of the transformations matter. Plot each transformed unit square. Note: the unit square has vertices (0,0), (1,0), (1,1) and (0,1).

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) This question concerns transformations using matrix multiplication. (i) Formulate the matrix that will first rotate by n/3 radians, then scale by a factor of 2 in the x direction. (ii) Formulate the matrix that will first scale by a factor of 2 in the x direction, then rotate by 1/3 radians. (iii) By applying these transformation matrices to the unit square, show that the order of the transformations matter. Plot each transformed unit square. Note: the unit square has vertices (0,0), (1,0), (1,1) and (0,1).
Transcribed Image Text:(a) This question concerns transformations using matrix multiplication. (i) Formulate the matrix that will first rotate by n/3 radians, then scale by a factor of 2 in the x direction. (ii) Formulate the matrix that will first scale by a factor of 2 in the x direction, then rotate by 1/3 radians. (iii) By applying these transformation matrices to the unit square, show that the order of the transformations matter. Plot each transformed unit square. Note: the unit square has vertices (0,0), (1,0), (1,1) and (0,1).
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