Determine if the following sets with operations are groups: (a) R with the operation given by r* y = -1- y. (b) The subset of R³ given by H = {(r, y, 2) E R° | x + y + z = 0}, with the operation (x, y, 2) + (a, b, c) = (r+a, y+ b, z + c).

Determine if the following sets with operations are groups: (a) R with the operation given by r* y = -1- y. (b) The subset of R³ given by H = {(r, y, 2) E R° | x + y + z = 0}, with the operation (x, y, 2) + (a, b, c) = (r+a, y+ b, z + c).

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

Determine if the following sets with operations are groups:
(a) R with the operation given by r * y = -1 - y.
(b) The subset of R® given by
H = {(r,y, 2) € R* |x+ y+z = 0},
with the operation (x, y, 2) + (a, b, c) = (r +a, y +b, z + c).

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