Topic: VECTOR SPACES Page No.......
Objective:
Out Comes:
nay Operation o Set !
Cpty Set.
Then G X G=} la, b); ac G,beG f
f! G x G ’G, theu f is Sald to be a
na opezation on the Set G.
Fo EoccwLale! +, X, , 0, * etc, s
biney opeotins on a Set.
d e . (+) heil be a binay opeatian
On G f tb e G) , b e G,
There a2e too
Tnte7nal Benesy gRortion l
enply Set , if
Then s called hteyal binay
opezatio G.
pezatiom
tet V
ncl be too on -
uf a ef d V theu eupty Sets
wniqlee theu * s called C
, Page No..
eaternel binay operation on V onerF.
Alqebraic stzuctu2e ii
Cmnpty set S eqcuippec eth
A Non called
binasy gperations is
algelraic Stuctwe.
Fo Cxaniple:(N,+).(Rit, ) ae algabuk
Structres
GROUP
alggebnaie Structe (Go,x)
Callecl p 0up. if binay operatim *
Scactisfies the follouwig dawe 'r
) CloSue daw! Fa9 a, b EG a b G
4 a, b E G.
i) Associatine daw. Fas) a, b c
a, b,c G
cc)Eaistence of oight
clentity !Thee, Gail
Cn eleuetecG,Such
that ate =a
e s
aEG. Tho clLsCh
Called the
ouzght icleutity
, ) Cacistence of right inuense ' Page No......
Each eleeut of GG posse Ees
Sight innentee.fon each clemebl
ae G dhere exsts ae eleent aeG
Tie eleue t is called the
enuese of a.
’ Abelicn Ginep of Conmutatine Gon0p:
AGop G us Sacel to be asel'
a Conmmutatine uf Comntatine law
is also Satisfied !
Commetatine aw a b b* a,beG
Fo Geaple i
(I.+)s cbelicn grop, whe
I s cthe Set of ntergersi
An Algebnale Structune (Ft,) s Caled
field. if ct is Sa
Postulas i
Satisfied the fllowg
Objective:
Out Comes:
nay Operation o Set !
Cpty Set.
Then G X G=} la, b); ac G,beG f
f! G x G ’G, theu f is Sald to be a
na opezation on the Set G.
Fo EoccwLale! +, X, , 0, * etc, s
biney opeotins on a Set.
d e . (+) heil be a binay opeatian
On G f tb e G) , b e G,
There a2e too
Tnte7nal Benesy gRortion l
enply Set , if
Then s called hteyal binay
opezatio G.
pezatiom
tet V
ncl be too on -
uf a ef d V theu eupty Sets
wniqlee theu * s called C
, Page No..
eaternel binay operation on V onerF.
Alqebraic stzuctu2e ii
Cmnpty set S eqcuippec eth
A Non called
binasy gperations is
algelraic Stuctwe.
Fo Cxaniple:(N,+).(Rit, ) ae algabuk
Structres
GROUP
alggebnaie Structe (Go,x)
Callecl p 0up. if binay operatim *
Scactisfies the follouwig dawe 'r
) CloSue daw! Fa9 a, b EG a b G
4 a, b E G.
i) Associatine daw. Fas) a, b c
a, b,c G
cc)Eaistence of oight
clentity !Thee, Gail
Cn eleuetecG,Such
that ate =a
e s
aEG. Tho clLsCh
Called the
ouzght icleutity
, ) Cacistence of right inuense ' Page No......
Each eleeut of GG posse Ees
Sight innentee.fon each clemebl
ae G dhere exsts ae eleent aeG
Tie eleue t is called the
enuese of a.
’ Abelicn Ginep of Conmutatine Gon0p:
AGop G us Sacel to be asel'
a Conmmutatine uf Comntatine law
is also Satisfied !
Commetatine aw a b b* a,beG
Fo Geaple i
(I.+)s cbelicn grop, whe
I s cthe Set of ntergersi
An Algebnale Structune (Ft,) s Caled
field. if ct is Sa
Postulas i
Satisfied the fllowg
