Q#1 Let T,: R2 → R² be the linear operators given by the formulasT, (х, у) %3D (х + у,х — у),T2(x, y) = (2x + y, x – 2y)(a) Show that T, and T2 are one to one.(b) Find formula for T¡ (x,y), Tz²(x, y) and (T20T1)~(x, y).(c) Verify (T,oT,)-1 = T,%oT;'.

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Q#1 Let T,: R2 → R² be the linear operators given by the formulas T, (х, у) %3D (х + у,х — у), Т, (х, у) %3 (2х + у, х — 2у) (a) Show that T, and T2 are one to one. (b) Find formula for T†'(x,y), T7'(x,y) and (T2ºT,)¯(x,y). (c) Verify (T,oT,)-1 = T,%oT;'.

Q#1 Let T,: R2 → R² be the linear operators given by the formulas T, (х, у) %3D (х + у,х — у), Т, (х, у) %3 (2х + у, х — 2у) (a) Show that T, and T2 are one to one. (b) Find formula for T†'(x,y), T7'(x,y) and (T2ºT,)¯(x,y). (c) Verify (T,oT,)-1 = T,%oT;'.

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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Q#1 Let T,: R2 → R² be the linear operators given by the formulas
T, (х, у) %3D (х + у,х — у),
T2(x, y) = (2x + y, x – 2y)
(a) Show that T, and T2 are one to one.
(b) Find formula for T¡ (x,y), Tz²(x, y) and (T20T1)~(x, y).
(c) Verify (T,oT,)-1 = T,%oT;'.

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