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• 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

• 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

Advanced Engineering Mathematics
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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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
Transcribed Image Text: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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