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) | сө — —Ө = -0 (reflection across origin) • Draw pictures describing the actions of linear maps A, B and C and the compositions AB, BA, АС, СА, ВС, СВ. • Which pairs of these maps commute. • Which are correct identities and why i) A² = C ii) C² =1 ii) A* : I, A5 = I_iv) B² = I v) B³ = B

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
origin)
• Draw pictures describing the
actions of linear maps A, B and C
and the compositions AB, BA,
АС, СА, ВС, СВ.
(reflection across
• Which pairs of these maps
commute.
• Which are correct identities and
why
i) A² = C ii) C² =I ii) Aª =
I, A5 = I 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 origin) • Draw pictures describing the actions of linear maps A, B and C and the compositions AB, BA, АС, СА, ВС, СВ. (reflection across • Which pairs of these maps commute. • Which are correct identities and why i) A² = C ii) C² =I ii) Aª = I, A5 = I iv) B² = I v) B³ = B
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