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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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).
Transcribed Image Text: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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