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Compute the 2 x 2 matrices associated to each of the following linear transformations. Treat each problem part as a new transformation! (a) Reflection about the y-axis. (b) Rotation clockwise about the origin by radians. (c) A horizontal shear by a factor of 3, that is, each vector is horizontally stretched by a factor of 3, but no change in the vertical direction. (d) Applying the transformations (c), then (a), and then (b) in that order. Not a typo!

Compute the 2 x 2 matrices associated to each of the following linear transformations. Treat each problem part as a new transformation! (a) Reflection about the y-axis. (b) Rotation clockwise about the origin by radians. (c) A horizontal shear by a factor of 3, that is, each vector is horizontally stretched by a factor of 3, but no change in the vertical direction. (d) Applying the transformations (c), then (a), and then (b) in that order. Not a typo!

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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7. Compute the 2 x 2 matrices associated to each of the following linear transformations. Treat each problem part as a new transformation! (a) Reflection about the y-axis. (b) Rotation clockwise about the origin by radians. (c) A horizontal shear by a factor of 3, that is, each vector is horizontally stretched by a factor of 3, but no change in the vertical direction. (d) Applying the transformations (c), then (a), and then (b) in that order. Not a typo!
Transcribed Image Text:7. Compute the 2 x 2 matrices associated to each of the following linear transformations. Treat each problem part as a new transformation! (a) Reflection about the y-axis. (b) Rotation clockwise about the origin by radians. (c) A horizontal shear by a factor of 3, that is, each vector is horizontally stretched by a factor of 3, but no change in the vertical direction. (d) Applying the transformations (c), then (a), and then (b) in that order. Not a typo!
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