Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)
Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)
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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Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)
![a*b
atb
ab
k
a米の米-、米a
ka
- 1
- a
There is an somorphism of Ug mith Zg in which 3=e'
Find the ekment in Zs hat coresponds to 3" for cach
M=0,1, -
Let i Ug-)Zg be the isormorphism where il7)=5
By te lomormuphiom paperty d ismphins il7)= i(3 3) = i(7) -, (3)
= 5+,5 - 2
%3D
i(7') = il7") +, i(7) = 2+5 = 7
i(7") = i(7') +s i(7) = 7+g 5=4
i(3) = il7")*s i(3)= 4 +5=1°
il7)= il7)+, il7)= 1l+, 5 = 6
i(3*)= i(3")*n i(3)= G t3 5- 3
i(3") = i(3?) = ¿(3")te il3)= 3+, 5 = 0 0
Def: Let <G, ,,) sd <Gs, B) be geaps and f.G,>G- We say fis
(1) f ó a bijective mp
(a) for all a,beG,, flax, b)= f(=) x, f(b),
[0,6)
Lo, c)
Ex: Find a bijective furction fram Ry to R. for any b,ce R".
Hence R.R su for
ceR
my
Let f: Ry-7R be defined as f(t)= g (t)
Injecine : Let toste ER and suppre fit.) -flt,)
Sajective: Sappose D c, R..](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67a79aa2-f715-406c-8bee-8178252bb86d%2Fcd295b5f-7933-47d2-9928-208af83c184a%2Fx2ki31n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a*b
atb
ab
k
a米の米-、米a
ka
- 1
- a
There is an somorphism of Ug mith Zg in which 3=e'
Find the ekment in Zs hat coresponds to 3" for cach
M=0,1, -
Let i Ug-)Zg be the isormorphism where il7)=5
By te lomormuphiom paperty d ismphins il7)= i(3 3) = i(7) -, (3)
= 5+,5 - 2
%3D
i(7') = il7") +, i(7) = 2+5 = 7
i(7") = i(7') +s i(7) = 7+g 5=4
i(3) = il7")*s i(3)= 4 +5=1°
il7)= il7)+, il7)= 1l+, 5 = 6
i(3*)= i(3")*n i(3)= G t3 5- 3
i(3") = i(3?) = ¿(3")te il3)= 3+, 5 = 0 0
Def: Let <G, ,,) sd <Gs, B) be geaps and f.G,>G- We say fis
(1) f ó a bijective mp
(a) for all a,beG,, flax, b)= f(=) x, f(b),
[0,6)
Lo, c)
Ex: Find a bijective furction fram Ry to R. for any b,ce R".
Hence R.R su for
ceR
my
Let f: Ry-7R be defined as f(t)= g (t)
Injecine : Let toste ER and suppre fit.) -flt,)
Sajective: Sappose D c, R..
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