polic1. Is T(z) = -z a translation, dilation, rotation, or none of the above?2. Show that the general linear transformation T(z) = az + b, where a and barecomplex constants, is the composition of a rotation, followed by a dilation,followed by a translation.▼ HintView the complex constant a in polar form.L3. Prove that a general linear transformation maps circles to circles.

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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 76E: A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h...

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Similar questions

A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
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1. Is T(z) =-z a translation, dilation, rotation, or none of the above?