Check that each of the applications follows linear transformations. a) Reflection Rr(x, y) with respect to a line r passing through the origin: let r be given Reflection Rr(x, y) with respect to a line r passing through the origin: let r be givenby the vector equation (x, y) = t(a, b), then Rr : R² → R² is given by Rr(x, y) = (a2-b2/a2+b2 . x + 2ab/a2+b2 . y, 2ab/a2+b2 .x + b2 - a2/a2+b2 . y) where (a, b) is any vector in the direction of r and (x, y) ∈ R2.b) Translation: T: R2 → R2 such that T(x, y) = (x + a, y + b), where a, b ∈ R e (x,y) ∈ R2.(Images about the questions below) (b) Translação: T : R? → R? tal que T(x, y) = (x + a, y + b), onde a, b e Re(x, y) E R². (a) Reflexão R,(x, y) em relação a uma reta r que passa pela origem: seja r dadapela equação vetorial (x, y) = t(a, b), então R, : R? → R² é dada por R,(x, y) =a² – b²2ab2abb? – a?·y), onde (a, b) é qualquer vetora² + 62a2 + 62a2 + b?a2 + b2na direção de r e (x, y) € R².

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Answered: Check that each of the applications…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Check that each of the applications follows linear transformations.

a) Reflection R_r(x, y) with respect to a line r passing through the origin: let r be given Reflection R_r(x, y) with respect to a line r passing through the origin: let r be given
by the vector equation (x, y) = t(a, b), then R_r : R^² → R^² is given by R_r(x, y) = (a²-b²/a²+b². x + 2ab/a²+b². y, 2ab/a²+b².x + b²- a²/a²+b² . y) where (a, b) is any vector in the direction of r and (x, y) ∈ R².