c) Let A, B and C be linear maps from the two dimensional plane to the plane given in terms of stan dard I, j basis vectors by Ai-j, Aj=i (anti clock wise rotation 90 degree) BE-i, Bj=j (reflection across vertical axis) CO=-0 (reflection across origin) Draw pictures describing the actions of linear maps A, B and C and the compositions AB, BA, AC, CA, BC, CB. • Which pairs of these maps commute. • Which are correct identities and why i) A=C i) C=1 ii) A'=I1, A=I iv) B =I v) B =B

c) Let A, B and C be linear maps from the two dimensional plane to the plane given in terms of stan dard I, j basis vectors by Ai-j, Aj=i (anti clock wise rotation 90 degree) BE-i, Bj=j (reflection across vertical axis) CO=-0 (reflection across origin) Draw pictures describing the actions of linear maps A, B and C and the compositions AB, BA, AC, CA, BC, CB. • Which pairs of these maps commute. • Which are correct identities and why i) A=C i) C=1 ii) A'=I1, A=I iv) B =I v) B =B

Name: c) Let A, B and C be linear maps fr om the two dimensional plane to t
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Description: c) Let A, B and C be linear maps fr om the two dimensional plane to the plane givenin terms of stan dard I, j basis vectors byAi-j, Aj=i (anti clock wise rotation 90 degree)BF-i, Bj=j (reflection acr oss vertical axis)CO=-0(reflection across origin)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

c) Let A, B and C be linear maps fr om the two dimensional plane to the plane given
in terms of stan dard I, j basis vectors by
Ai-j, Aj=i (anti clock wise rotation 90 degree)
BF-i, Bj=j (reflection acr oss vertical axis)
CO=-0
(reflection across origin)
Draw pictures describing the actions of linear maps A, B and C and the
compositions AВ, ВА, АС, СА, ВС, СВ.
• Which pairs of these maps commute.
• Which are correct identities and why
i) A=C i) C=1
ii) A=1, A=I iv) B=Iv) B=B

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