Let R9:R2 → R² is a linear transformation rotation function, where 0 is an angle of the[cos 0Lsin 0- sincos e is a standard matric of Rg, such that R9(V) = AV.rotation, and let ACOSa) sketch the vectors v,V2 = |4b) Rotate v,, and v, about the origin, through 0 =" (counterclockwise).2

This is a problem of linear transformation.

Answered: Let Re:R → R² is a linear…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 45E: Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a...

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Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
Find a basis for R2 that includes the vector (2,2).
For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
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Let Re:R → R² is a linear transformation rotation function, where 0 is an angle of th Гcos ® -sin 0 – sin 0j is a standard matric of Re, such that Re(V) = AV. rotation, and let A : COS a) sketch the vectors v, = 1, Зп b) Rotate vị, and v, about the origin, through 0 ( counterclockwise).