Define a linear operator (transformation) on R2 by performing the following operations in order: (i) a rotation by an angle of π/4 clockwise, (ii) an orthogonal projection onto the vector u = = (1, 1), and (iii) a compression in the x-direction by a factor of 2. Compute the standard matrix of this operator.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Define a linear operator (transformation) on R2 by performing the following operations in order:
(i) a rotation by an angle of π/4 clockwise,
(ii) an orthogonal projection onto the vector u = = (1, 1), and
(iii) a compression in the x-direction by a factor of 2.
Compute the standard matrix of this operator.
Transcribed Image Text:Define a linear operator (transformation) on R2 by performing the following operations in order: (i) a rotation by an angle of π/4 clockwise, (ii) an orthogonal projection onto the vector u = = (1, 1), and (iii) a compression in the x-direction by a factor of 2. Compute the standard matrix of this operator.
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