(i) Find the matrix that represents the reflection g in the linethrough the origin with angle of inclination 165°.(ii)The matrix that represents the rotation h through 90° aboutthe origin is0(i-1)Show that the composite transformation formed from therotation h followed by the reflection g is the reflection in theline y = -√3x.

Answered: Image /qna-images/answer/6a2fbfd0-5239-477b-8748-6f1829f4175a.jpg

Answered: (i) Find the matrix that represents the…

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 47E

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Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Find the standard matrix of the composite transformation from R2 to R2. Counterclockwise rotation through 60°, followed by reflection in the line y = x
1) Derive the matrix that performs the following consecutive transformations(in augmented form):1- Translation of 2 units along x-axis.2- Rotation by 90° about z-axis.3- Rotation by 90° about y-axis.
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(a) Find a single matrix that defines a rotation of the plane through an angle of -(π/4) about the origin and moves twice their original distance from the origin.(b) sketch the image of the unit square under the transformation from part (a)
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