Let S be the set S= {a+bk : a,b ER}, where k is a formal symbol. Define addition and multiplication operations on S as follows: given elements x = a+bk and y =c+dk in S, x+y:= (a+c)+ (b+d)k, xy:= (ac+ bd)+(ad+bc)k.
Let S be the set S= {a+bk : a,b ER}, where k is a formal symbol. Define addition and multiplication operations on S as follows: given elements x = a+bk and y =c+dk in S, x+y:= (a+c)+ (b+d)k, xy:= (ac+ bd)+(ad+bc)k.
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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a) prove by identity. include a short explanation of how you know what the indemnity elements are.
b) prove that the multiplicative inverse law is false for s. (don’t just write down a counter example; also prove that your counter example is valid)
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