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2. A linear transformation defined by a diagonal matrix whose diagonal entries are positive is called a magnification. Consider the magnification defined by the matrix A = 2 [83] 0 (a) Find the image of the triangle with vertices (1, 0), (0, 1) and (2, 2) under the magnification defined by A. Sketch the original triangle as well as the image of the triangle under the magnification. (Hint: The images of the position vectors for each of the three vertices will correspond to the position vectors for the vertices of the image of the triangle.) (b) Now find the image of the magnified triangle (from (a)) under the linear transformation of counterclockwise rotation by an angle of. Sketch the magnified triangle as well as the rotated triangle.

2. A linear transformation defined by a diagonal matrix whose diagonal entries are positive is called a magnification. Consider the magnification defined by the matrix A = 2 [83] 0 (a) Find the image of the triangle with vertices (1, 0), (0, 1) and (2, 2) under the magnification defined by A. Sketch the original triangle as well as the image of the triangle under the magnification. (Hint: The images of the position vectors for each of the three vertices will correspond to the position vectors for the vertices of the image of the triangle.) (b) Now find the image of the magnified triangle (from (a)) under the linear transformation of counterclockwise rotation by an angle of. Sketch the magnified triangle as well as the rotated triangle.

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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2. A linear transformation defined by a diagonal matrix whose diagonal entries are positive is called a magnification. Consider the magnification defined by the matrix A = 2 0 0 3 (a) Find the image of the triangle with vertices (1,0), (0, 1) and (2, 2) under the magnification defined by A. Sketch the original triangle as well as the image of the triangle under the magnification. (Hint: The images of the position vectors for each of the three vertices will correspond to the position vectors for the vertices of the image of the triangle.) (b) Now find the image of the magnified triangle (from (a)) under the linear transformation of counterclockwise rotation by an angle of. Sketch the magnified triangle as well as the rotated triangle.
Transcribed Image Text:2. A linear transformation defined by a diagonal matrix whose diagonal entries are positive is called a magnification. Consider the magnification defined by the matrix A = 2 0 0 3 (a) Find the image of the triangle with vertices (1,0), (0, 1) and (2, 2) under the magnification defined by A. Sketch the original triangle as well as the image of the triangle under the magnification. (Hint: The images of the position vectors for each of the three vertices will correspond to the position vectors for the vertices of the image of the triangle.) (b) Now find the image of the magnified triangle (from (a)) under the linear transformation of counterclockwise rotation by an angle of. Sketch the magnified triangle as well as the rotated triangle.
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