Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 5 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 3 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 17CM
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Find a single matrix for the transformation that is equivalent to doing the following four transformations of
the plane in succession:
1. Shear by a factor of 5 in the x-direction.
2. Reflection over the line y = x.
3. Expand by a factor of 3 in the y-direction.
4. Rotate counter-clockwise by 90 degrees.
Transcribed Image Text:Find a single matrix for the transformation that is equivalent to doing the following four transformations of the plane in succession: 1. Shear by a factor of 5 in the x-direction. 2. Reflection over the line y = x. 3. Expand by a factor of 3 in the y-direction. 4. Rotate counter-clockwise by 90 degrees.
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