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The context of this question is linear transformations on the plane R². Let T: R² → R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.

The context of this question is linear transformations on the plane R². Let T: R² → R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 12CM
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2. The context of this question is linear transformations on the plane R². Let 7: R² R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.
Transcribed Image Text:2. The context of this question is linear transformations on the plane R². Let 7: R² R² be the function defined by first rotating the vector counter-clockwise by an angle of 45° and then stretching by a factor of 5 in the direction of the x-axis, and by a factor of 2 in the direction of the y-axis. Explain why T is a linear transformation and find the matrix associated to T.
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