e) Let W = {(x; y) x,yER}. Define addition and scalar multiplication %3D a + B = (x; y) + (a ; b) = (x + a + 1; y + b -1) = k(x ; y) k a = (x +k; y) %3D = (a + B) + Y for a,B, Y e W a + (B + Y) 3 0 EW such that a + 0 = 0 + a = a, a e W k( a+ B) = ka + kß, a ß e W, keR a) b) c) %3D

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
e)
Let W = {(x; y) |x, y ER}. Define addition and scalar multiplication on W
a + B = (x; y) + (a ; b) = (x + a + 1; y +b -1)
kαk(x , y)
a + (B + Y)
3 0 EW such that a +0 = 0 + a = a, a e W
k( a+ B) = ka + kß, a ‚ß e W, ke R
= (x+k; y)
(a + B) + Y for a B,y e W
a)
%3D
b)
%3D
c)
%3D
Transcribed Image Text:e) Let W = {(x; y) |x, y ER}. Define addition and scalar multiplication on W a + B = (x; y) + (a ; b) = (x + a + 1; y +b -1) kαk(x , y) a + (B + Y) 3 0 EW such that a +0 = 0 + a = a, a e W k( a+ B) = ka + kß, a ‚ß e W, ke R = (x+k; y) (a + B) + Y for a B,y e W a) %3D b) %3D c) %3D
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