Let T/6 : R² → R² denote the linear transformation which rotates a vector in R- counterclockwise by T/6 radians. Let Tref : R² → R² be the linear transformation which across the line x1 = x2. x2 reflects a vector x = (a) Sketch a cartoon illustrating what these linear transformations do to the vector e1 = (b) Find the standard matrices of T/6 and Tref. (c) Find a nonzero vector v E R² such that Tz/6 © Tref (v) = T,ref o Ta/6(v) or explain why no such vector exists.

Let T/6 : R² → R² denote the linear transformation which rotates a vector in R- counterclockwise by T/6 radians. Let Tref : R² → R² be the linear transformation which across the line x1 = x2. x2 reflects a vector x = (a) Sketch a cartoon illustrating what these linear transformations do to the vector e1 = (b) Find the standard matrices of T/6 and Tref. (c) Find a nonzero vector v E R² such that Tz/6 © Tref (v) = T,ref o Ta/6(v) or explain why no such vector exists.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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