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d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, + a 1; ay, - 2a + 2) = (a + B) + Y 30 εK such that α+0- 0+ α- α, α εκ. a®(x;;y,) = 1. a + (B + Y) for a B, y €K 2. 3. k( a+ B) = ka + kß, a ,ß e K, ke R 4. (k + m)¤ = ka + ma, ɑ e K, k,m e R %3D

d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, + a 1; ay, - 2a + 2) = (a + B) + Y 30 εK such that α+0- 0+ α- α, α εκ. a®(x;;y,) = 1. a + (B + Y) for a B, y €K 2. 3. k( a+ B) = ka + kß, a ,ß e K, ke R 4. (k + m)¤ = ka + ma, ɑ e K, k,m e R %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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d). Let K = {(x;y) | x,y € R} with operations (x1;y) © (x2;y2) = (x, + x2 + 1; y, + y2 - 2) %3! a®(x;;y1) = (ax, + a - 1; ay, - 2a + 2) (a + B) + Y for a,B, y EK a + (B + Y) 30 ΕK such that α +0- 0+α-α , α εΚ ( a β ) - ka + kβ , α ,β εΚ , k R (k + m)a = ka + mœ, ɑ e K, k,m e R %3D %3D -am 4.
Transcribed Image Text:d). Let K = {(x;y) | x,y € R} with operations (x1;y) © (x2;y2) = (x, + x2 + 1; y, + y2 - 2) %3! a®(x;;y1) = (ax, + a - 1; ay, - 2a + 2) (a + B) + Y for a,B, y EK a + (B + Y) 30 ΕK such that α +0- 0+α-α , α εΚ ( a β ) - ka + kβ , α ,β εΚ , k R (k + m)a = ka + mœ, ɑ e K, k,m e R %3D %3D -am 4.
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