Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Linear transformations can be used in computer graphics to modify certain shapes. Consider the linear transformation T: R2 R2 below such that T(A) = B, where A represents the square and B the parallelogram below. 1 1 B 1 1 y. y 1 1 2 X T
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Transcribed Image Text:Linear transformations can be used in computer graphics to modify certain shapes. Consider the linear transformation T: R2 R2 below such that T(A) = B, where A represents the square and B the parallelogram below. 1 1 B 1 1 y. y 1 1 2 X T
1 2 x (4a) Find the matrix of T. (4b) Apply the linear transformation T to C (the triangle below) and plot D = = T(C)? (4c) Does the linear transformation T preserve the area in the two examples shown? Does it preserve the perimeter? (4d) Does the linear transformation T preserve the area of every triangle? Does it preserve the perimeter of every triangle? Justify your answers.
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Transcribed Image Text:1 2 x (4a) Find the matrix of T. (4b) Apply the linear transformation T to C (the triangle below) and plot D = = T(C)? (4c) Does the linear transformation T preserve the area in the two examples shown? Does it preserve the perimeter? (4d) Does the linear transformation T preserve the area of every triangle? Does it preserve the perimeter of every triangle? Justify your answers.
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