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/''
o.a.u.-- FEN vE BoBgiyar parurrssi
NaatsMArirsOua/ru
^e
,,.t d";f
Matel!&-
-F'*
' - Final Srnavr
Matematik
So1'ut
2? Haztrat2009
Siire: 11odk
isim
Ogrenci no.
imza
29
sl
31)
54-l5p
53 -20p
S2- 20p
-,15p
55
-l5p
s7- 16
56- 20p
f :A->B olsun. Her a,beAiqin a-bef(r)=f(t)
Toplam:
iletarurnir
-
ba[mtrsrmnbirdenklik
balrntrsr oldulunu g6sterip denklik smrflanm bulunuz.
)
t ,,
1^..{
-.--
t ,ur c^
q
O\N
,
)
,.,r
t."'\'
9, S,*'t4t''.,
l-4
\SL
f7
-...
4ix\ = 1ta')
L"' u- Ao-Uaw(ur
o\o..
=
{tt)
{i*r
{tt\ = {ta
)
J,
Cegl'1n'',
cr.-b
-f to') =
LruC iSe
ve
rt,..l
L o(u;-
-/e- {tu) = { {c)
{Lb)
,n Lr 7
o\,;r
."
.
4tc"\
=
{(c)
\i)
idl v",,o.J: x
{,o=
52)
iiaerinde
.9 kiimesi
var mr?
a,t 6 = ab + a + b
)
(ti(b = L*a
,
6r''+(\t
t2
(ct.uU)
=
t,..+
t
r-a.
/
c,\eRlwre\,
\.\ir
-+J_
6itc..a.1 La1 6l *
I
c'+DlC'
{c.L+n1t)c1 Cr-},*cr,.l+c .,
c\* (Uc1t1c) , 6!bc- b+c) <o11tcn-t-c)
*c
(r"L+ctt!) x
ax Ibxc)
C
--Jq
i--vc\ct
C"bt v ''''" '
&r9= oe<f,tt- =d
e(
\+a) =
L'- o /
€-*
(L
O 6/
=
t/
ecr-rEt(=R
/
e-(
i+a-\ - o
-,--
'R,'i'*
€,\uw'..c'"r"
9:{ urcL'r
bc
r- r''' 1t24'C
'
53) a) Agaltdaki kiimelerden hangileri birer alt-grup tur?
i)
{1,-1}c R.
ii) Znn,
pozitif tam sayrlar alrkiimesi , i{ow. Jt:
vl' i, ") .,0=n* ,
\.u e R di/
1t)
@
-.4\
o)
3-
--
qo-.* aI*
C / ,{
ou
-ff*l
zv t\
(a'nl
@a,, 1,4w3
la.\
"^ )
g*" A nS,'\L'.fAl'lrk
)
ev
'l\
?.<
'i*
I
,qu
l
,n leJe,
.-t- X
3'^ e G
r.t)
/,,
3
ConVi,t
)
(Hatnlafina: (a, D)
la,b\
-
."
.
3o.
L.z
[rU,
e
ad=bc)
U,)
)-
(ct, Ar
--)
lA)
(arJr1
.,".'j
o
h)rbc\ttJ'
\'
'i":i
,^*(5rA
ql
)
)',se )l a,bl+ kp) L (d,ayr 1rt,4r
cdl =
'trct
( ., d
ve-
a.bt= bal,L
p,l1uc,
zr(s\u\
-,r ^ ?o ?9.2
5
,l*1H?
\--\
toplama igleminin iyi tanmh oldu[unu gdsteriniz.
(c, a)
{)i= :
(rr
dr.(.
da tanmlanan
t,
d$ld,r_,
ise (G,.) cebirsel yaprsuun grup oldu[unu giisteriniz.
- .L e G dJr.
o{
'5"
olduSt't{tt
rin lrif, -
$,t'* de.**
3*.3-*
54) Q
-llw
q^F*
-.---U--
C={f I xeZ\
z,
,
G=A , lt= tvc -|"r* t "6il*
,I ;,P
C7U;
l.
4 d;. l'( qwl\.'^Ya
1'\n hd, 1 / -{
06r(
'r{rru , iR*,.. Ur, 0,.)*- qr,rb"d,'C
Upufi,Urg.i
'|
t
otsu-A
ll- l l,-ll
U.',
(
Lt/lt)
5/
tJ[ atJ.!.')
j0x^@.
t9t
Tam sayrlarda sralama:
H", o=@n
b=@A c=@,p)ez
ac)-ab
=
).- irv',n1
.-,
TdF
gOsteriniz.
c> b
oldufunri
-(-
ot* k-(
/
znaa
lo/
n+t=s
\,).-
I
.t ( o+'r.)
(;,i
A*
qi) t
?,
u ?,,^
*'si q
x)
oldu[.unu sosteriniz.
fr+&=(
X'Y'
) ?ua^ 'Pri'
=
ll =\*'y's,
{xt b
I X= 6
|-=-
b) Her (ag) e z iqi,
t\
.-
] (-',ur\I,.
GD.GD
= (x,
[rtxltx, a'*ty):
axlLx+x
$^,"i
a
[a.v+tr,
[*,x)
AxtLx+x
'bo
(
.[t
(unb;
.Lr; 51
axltx),- U,v-\ 2
1-
ax+Lx, o.x"Lx)
L*t tkf
+z:W*
f**.[uO J
v."r
2 y'rv"t.
f
jtil 2n k (I** ) t
91zu
Qf
aenneminleortintir.-
l--l)a
l,r
0+tt
l.
k(o+*)+
a)
iein
,-
?)
56)
a>0
ve
= (xrx)
6-7
o
L>q
6u \.'.rnl,.r.
f
II
-(r+
D.A.u.-- FEN VE eOesiyAr FerUrrBSi
MATEMATIT gOTUMU
t\[atelll
Soyut
7
Matematik -
X'inal Smavr
Hazlrm2010
Silre:
Isim
Of,renci no.
Sl -15p
52- 30p
33
-i5p
Sl) x,yeN ign x*y=y4y2
54-15p
ve
36- lsp
35 -20p
x"!=x!2
iletamml
Toplam:
ise,
a-) * i$leminin " iqlemi iizerine safdan ve soldan daprlma dzellifi var mr?
b-) . iglemi birleSmeli mi? Belirtiniz.
a)
= * (5*l =
6) .' (xx1)o(xrz\ = [rt*
-1 x*{yoz)
x+[gz.f
x
[xo5)r? =?
Or;r * t =
lXxe)
o
llodk
Imza
(
x+ $z'?
o (x* z")
'rdfr.
-1
(xtf ) (xr z')" J
U"t\
r*{ -'_-g:2' (...$
$t,\qr^d.,
,1(!
/o
52)
a-) G
deEi$me
iizelli$ olan bir gnrp ve
= ^tszL
11
={x
ecl r-' = r} is., }I,
-
d,qr0
G nin iginde bir gnrp (alt-grup)
olur mu, belirtiniz.
O uLrc
e). e
--)
"el'(
du. L
C YeKrst x4el( ^d,,1
G)Her a,b eG iqin, (abl'=
@
a'?D'z
(4=
x w (*uf' :? t''
I '- x4 k, .'- rnr 5,
esitliEini sallayan grubun de[igmeli oldu[unu
^h^h - ^z5u\6>
o-bnb
94a"^
9
= ^nLl>
bl,
gdsteilr.
G\-gS*r",,
Ll,
5.ldo-,t a1 rlP qotT-rol,
|o. = o6
1-
eu,a eirtit/
C flf-*t'-
rln
A
*rAgafrdaki kiimeler verilen iglemlere giire grup olur mu? Sebepleriyle
)'t (2X,.)
d;
s,nt4la.l o(dufa i5ia,
iqlnora
t
ii)
l)
iii) (2,,,,+l /
Lr.ran 0 L"L^
lt^V otrSrndo.lcr
'hr^ f-ao Snqbn
,C
| -
(2,,,.)
a$LL hoL^
A y,W"r, "z
-lo7l-.r'o'A^
do',v- olrna{t^fl tit^
agrklayrnrz.
o
D),r,4,n,.' tglrrvdl
lef
,
lo
\
ot.,'o.drnt,'dla,
U
r ( iit rz)n--=? (trtrt )+ilo+8 ='b+lt
',
,q=
53) Tam saylm ktimesinde
J.l^,6srjb
;)
-iu,be Uty
t*
U%
x-v<3olx-y
rl
ile tammh
ls=T.
6 =1 ttr --
l-r
o(e0l \d.^i.
;
.- r-l
O Stlo=t9=0 i.(S)=lo
1 i + tt --ts =A "'- (3)= tz v6-
Stn'l"rL'
asa-{ LoJo-n
e=b
att e 4e olrr.
olan ba[rntrmn bir denklik balurtrsr oldulunu giisterip, denklik surrflannr yazrnz.
u'
I
t,inti,
rlrc
tl
1n x.-rx r^id,r ? 8."a,
-'
*
-4
e
q
x.,a,n^,J*\
\)
J
r'0ul
b ve t^l? is.
@
-r
-\
.
Ib-'i"ia-^rJ A
-9"**tt
oo\ffi,,g,ff*e
6l
tr"
.,^'&r
'.
t
6
= l''[.]l )
). -tr, -t )o/L,t?)ty ,..
{L=/:?1 3i..433."J
r= {lct6
to
q = L .--2 )t4)
,
[=)
"'J?
I=
,i )l)1) l3,tL .,1
,I I
!e) lra l= I J,,-q / ztt),t J \
-lLtnn sn\\"n,
fus,.^-
t=,dr,
Yu?
rv
u
r
xat
t
w)
*
^l--n'
.1.
a 1r_u
.
/,,
.-,J
YtTd"t
C";s"*
.
I
1
I
60
''
"'
qu*trr
i
I
I
I
3
b
54) Rasyonel sayrlar kiimesi iizerinae
olduSunu giisteriniz.
Qlatrrlatmar (a, D) - (c, a) e ad = bc)
f", b)
-
@$-Qfi=@,U7
\^a
[c, A)
(a',A)
A:
(a"at, Lbt)
I l't
t
u G/,il)
(a,L)(ol,b'\
vu-
iyi tanrnh
)l Ir,llt',1) I
dJ-r =-4t.r
a-A.-bc
nir6rst
geklinde tanrmlanan garpmanm
lr
'7
an- ( cc/, dd,)
-?
5
uxf
4tbtcc'
al---bc
9n.Jri
atdt=
Ltcr
he 5.
dnr,
ss) a-) Sonsuz tane asal sayr oldu[unu gtisteriniz.
*ffglu,
0l-',.^''g,a
v
\.re
6.r.-
a--e,/"\
lLr
'l
l,.lL.l, -f" *
6\r p,9s! bdlo-
A?
deA;r.
?=
hme"j
lr
f
rts..!
'--, PI
so"drols
Jonl,,.
,
?,,
olsr..-...
,
1 *tb^
a>l
1_J
l,re \rrrs^dtlta\
v^rd*r,
?ru..o ? dqrl, t-
rl^ *
b-) 18lx+72y=20
i
r l,fr.-,1"
olacak gekilde
x,y
eZ
ttt.= 2-.1L
)1?+9?
19?
?z= 1,3\+i5
j],1,i(+2.
=
17.Lr
?-= 2.1+
f*
o
lA ui,""ds-,.'
,L" 66bn
?1"- ?'1, l^=
L
tam saylarrnr bulunuz.
(81
35
oid,tQ,,'nu larso,3o'L-w.
z^
,
'f
o-l r-rr-,,
h;-ri,n^
?lLA,7=tL
di u
Eeqbi
b'n
'tenq
!-.
39- 11.L.
= 39- tr(3?-
L.-.tatftrt,lz!
t.3s)
= 3t- l?.3)t t1-3(
= 18-39- tT.3i
O q
- le(+?-1.3?\ *\?.31
= 18.?z-
5 S+
- 16.?2- 3s(l&t - L+L)
L =-W.?Z'3g.tfl *
2.o = gt.?n:)Z- 3S.2r.l&l
-?oo. !et + t?60_?Z =?e
L,
I LG?e
o
l?t"+za
.
2o
56) p
asal ve
pla'
ise
f'la'
I l^a u'"
f)
oldufiunu gdsteriniz.
li* "g1
u Dr
,-u+[*LA
a;
I
l^ J'!.
e]tt\r.
,
.
(=) 7'L-a
,?
l"l'o^
?n
7lu
Ln.
^n=
(7DgY!' tPL) ={-L^r.
"
L ;,*
t
{1"^
,,
d1)o