c) Let A, B and C be linear maps from the two dimensional plane to the plane givenin terms of standard I, j basis vectors byAi=j, Aj=-i (anti clock wise rotation 90 degree)Bi=-i, Bj=j (reflection across vertical axis)ce = -0Draw pictures describing the actions of linear maps A, B and C and thecompositions Aв, ВА, АС, СА, ВС, СВ.(reflection across origin)• Which pairs of these maps commute.Which are correct identities and whyi) A? = c i) c² = 1 ii) A* = 1, 45 =1 iv) B² = I v) B³ = B

Answered: Image /qna-images/answer/ab60104b-32e8-481b-b658-8f9794fc52e0.jpg

Answered: • Which pairs of these maps commute.…

• Which pairs of these maps commute. Which are correct identities and why i) A? = c i) c² = 1 ii) A* = 1, A5 = 1 iv) B² = I v) B³ = B %3D

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Question

c) Let A, B and C be linear maps from the two dimensional plane to the plane given
in terms of standard I, j basis vectors by
Ai=j, Aj=-i (anti clock wise rotation 90 degree)
Bi=-i, Bj=j (reflection across vertical axis)
ce = -0
Draw pictures describing the actions of linear maps A, B and C and the
compositions Aв, ВА, АС, СА, ВС, СВ.
(reflection across origin)
• Which pairs of these maps commute.
Which are correct identities and why
i) A? = c i) c² = 1 ii) A* = 1, 45 =1 iv) B² = I v) B³ = B

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