bab6 transpor m
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prof.TRANSCRIPT
V BAB
ISATROPSNART EDOTEM 5 nauluhadneP .1.
macamreb tapadreT - utauS .)ledom krowten( nagniraj ledom macam
sirag metsis utaus halada nagniraj - narulas uata sirag - gnay narulas
kitit nakgnubuhgnem - halada nagniraj hotnoc aparebeB .nanialreb gnay kitit
nagniraj nagniraj nad ,ayar nalaj nagniraj ,apip narulas metsis ,ipa aterek ler
kitit irad sura idajret ,ini nagniraj aumes malaD .nagnabrenep - rebmus kitit
apip narulas metsis utaus malad ,aynlasiM .naujut kitit aparebeb ujunem
sag uata ,kaynim ,ria mirikid tapad gnay nanaggnal ujunem rebmus irad
.atnimem
halasam kaynaB - halasam iagabes naksumurid tapad nagniraj halasam
nakanuggnem nagned helorepid tapad aynisulos nad )PL( gnimmargorP raeniL
kinket kaynab ipateT .skelpmis edotem - halet susuhk nagniraj kinket
abmekid .skelpmis edotem adap irad neisife hibel aynmumu adap gnay nakgn
gnay nagniraj ledom irad hotnoc utas halas halada isatropsnart halasaM
iric ikilimem - .uti itrepes iric
5 isatropsnarT edoteM isinefeD .2.
nagned nagnubuhreb isatropsnart edotem ,aynmumu adaP isubirtsid
naujut aparebeb adapek )ylppus( rebmus aparebeb irad kudorp utaus
macam utas ada aynah aneraK .muminim isatropsnart ayaib nagned )dnamed(
irad aynnaatnimrep ihunemem tapad )dnamed( naujut tapmet utaus ,gnarab
.rebmus hibel uata utas
iriC - p iric :tukireb iagabes halada isatropsnart nalaosre
.a utnetret naujut halmujes nad rebmus halmujes tapadreT
.b nad rebmus paites irad nakisubirtsidid gnay gnarab/itidomok halmuj
utnetret aynraseb ,naujut paites helo atnimid gnay
.c us irad tukgnaid/mirikid gnay itidomoK ,naujut utaus ek rebmus uta
rebmus satisapak uata nad naatnimrep nagned iauses aynraseb
.d ,naujut utaus ek rebmus utaus irad itidomok natukgnagnep sokgnOutnetret aynraseb
5 isatropsnarT ledoM .3.
asim isartsuli utaus ,isatropsnart halasam naksalejnem kutnU ada aynl
itrepes nagniraj ledom utaus iagabes )3=n( naujut 3 nad )3=m( rebmus 3
:tukireb rabmag adap tahilret
5 rabmaG nagniraJ ledoM .1.
X( mirikid gnay halmuJ satisapaK ji nahutubeK ) rebmuS nad C( mirik sokgno ji naujuT )
C 11 X ; 11
C 21 X ; 21
C 31 X ; 31
C 12 X ; 12 C 22 X ; 22
C 32 X ; 32
C 13 X ; 13 C 23 X ; 23
C 33 X ; 33
iagabes halada ayngnimmargorp raenil alumrof akam ,naikimed nagneD
:tukireb
:nakmuminiM
C = Z 11 X 11 C+ 21 X 21 C+ 31 X 31 C+ 12 X 12 C+ 22 X 22 C+ 32 X 32 C+ 13 X 13 C+ 23 X 23 C+ 33 X 33
X 11 X+ 21 X+ 31 a = 1
X 12 X+ 22 X+ 32 a = 2 rebmus satabmeP
X 13 X+ 23 X+ 33 a = 3
X 11 X+ 12 X+ 13 b = 1
X 21 X+ 22 X+ 23 b = 2 naujut satabmeP
X 31 X+ 32 X+ 33 b = 3
:halada ayngnimmargorp raenil lebat nakgnadeS
a1 b1
a2
a3
b2
b3
lebaT 5 gnimmargorP raeniL .1.
Z X 11 X 21 X 31 X 12 X 22 X 32 X 13 X 23 X 33 isuloS
naujut naamasreP 1 -C 11 -C 21 -C 31 -C 12 -C 22 -C 32 -C 13 -C 23 -C 23 0
rebmus satabmeP 0
0
0
1 1 1 1 1 1 1 1 1
0 1 1 1 0 0 0 0 0
1 1 1 0 0 0 0 0 0
a1
a2
a3
naujut satabmeP 0
0
0
0 0 1 0 0 1 0 0 1
1 0 0 1 0 0 1 0 0
1 0 0 1 0 0 1 0 0
b1
b2
b3
lebat tahil( utas uata lon agrahreb naka sigolonket neisifeok aumeS
kadit sataid lebat iraD .isatropsnart ledom tafis nakapurem ini nad ,)sataid
es lawa isulos tahilid tapad isatropsnart nalaosrep adap uti anerak ,salej arac
.tukireb lebat nagned itnagid ipatet sataid itrepes lebat nakanugid igal kadit
lebaT 5 isatropsnarT nalaosreP skirtaM .2. naujuT
rebmuS
1
2
3
narawaneP
1
C 11 X 11
C 21 X 21
C 31 X 31
a1
2
C 12 X 12
C 22 X 22
C 32 X 32
a2
3
C 13 X 13
C 23 X 23
C 33 X 33
a3
naatnimreP
b1
b2
b3
,naikimed nagneD tapad ini isatropsnart nalaosrep nupualaw
tafis ipatet ,skelpmis edotem nagned nakiaselesid - ,uti susuhk gnay ayntafis
ulal satnipes gnay ,anahredes hibel huaj gnay rudesorp nususid tapad akam
nakaes - .skelpmis edotem nagned aynnagnubuh ada kadit naka
adA adap hararet aynaumes gnay ,isatropsnart edotem macam aparebeb
halasam irad lamitpo naiaseleynep - inisiD .idajret gnay isatropsnart halasam
IDOM edotem nagned naktujnalid ,enotS gnippetS edotem nakaracibid naka
.)MAV( dohteM noitamixorppA s’legoV nad
.1.3.5 gnippetS edoteM - enotS
gnippetS edotem nasalejnep hadumrepmem kutnU - naka enotS
:tukireb hotnoc nakakumekid
naahasureP .P nad ,H ,W id kirbap agit iaynupmem naahasurep utauS
kirbap irad ayniskudorp lisah isakola halasam ipadahgnem - ek tubesret kirbap
dug gna - gnadug nahutubek ,kirbap satisapaK .C nad ,B ,A id nalaujnep gnadug
adap tahilid tapad gnadug pait ek kirbap pait irad natukgnagnep ayaib nad
lebaT 5 ,3. 5 nad ,4. 5 .5.
lebaT 5 P nad ,H ,W kirbaP satisapaK .3. kirbaP malad( iskudorP satisapaK )not
W H P
09 06 05
halmuJ 002
lebaT 5 C nad ,B ,A gnaduG nahutubeK .4. gnaduG )not malad( naluB pait nahutubeK
A B C
05 011
04 halmuJ 002
lebaT 5 P .H ,W kirbaP irad noT paiteS natukgnagneP ayaiB .5. .C ,B ,A gnaduG ek
iraD )haipur naubir malad( not pait ayaiB A gnaduG eK B gnaduG eK C gnaduG eK
W kirbaP H kirbaP P kirbaP
02 51 52
5 02 01
8 01 91
isakolA lebaT nanusuyneP .a
,halasam nakhacemem nad imahamem hadum hibel kutnU sataid atad
satisapak aratna nagnubuh nakkujnunem gnay lebat utaus malad ek nususid
adap tahilret itrepes natukgnagnep ayaib nad ,gnadug nahutubek ,kirbap
lebaT 5 :tahilret tubesret lebat adaP .6.
pait nahutubek halmuJ - aret sirab adap nakkatelid gnadug pait rihk
rihkaret molok adap nakkatelid kirbap pait satisapaK
licek tapme iges adap nakkatelid natukgnagnep ayaiB
X ji A irad aynlasiM .j naujut ek i rebmus irad isakola aynkaynab halada
X = )1 naujut ek 1 rebmus( B ek 11 X ialiN . ji .iracid naka gnay halini
ebaT l 5 isatropsnarT lebaT .6.
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
W kirbaP
02 X 11
5 X 21
8 X 31
09
H kirbaP
51 X 12
02 X 22
01 X 32
06
P kirbaP
52 X 13
01 X 23
91 X 33
05
nahutubeK
gnaduG
05
011
04
002
isakolA rudesorP .b
ayntujnales hakgnal akam ,lebat kutneb malad nususret atad haleteS
d kudorp nakisakolagnem halada kirbap ira - gnadug ek kirbap - .gnadug
adap namodepreb amatrep sitamitsis isakola rudesorP tual tarab tudus
.)elur renroc tsewhtron( lebaT irad sata irik tudus irad ialuM 5 X( 6. 11 )
nad satisapak tahilem nagned kudorp mumiskam halmujes nakisakolaid
g nahutubek X alib ,uti haletes naidumeK .gnadu ji rihkaret katok nakapurem
X adap nakisakolagnem nagned naktujnalid ,hilipid gnay 1+J ,i iaynupmem i alib
X ek nakisakola ,kadit aliB .asisret gnay satisapak j,1+i aggnihes aynsuretes nad
.ihunepret halet nahutubek aumes
lebaT 5 gnadug ek kudorp amatrep pahat isakola lisah nakapurem .7. - gnadug
namodep nagned tual tarab tudus asaib isakola isiret gnay tapme igeS .
tubesid utab tapme iges tubesid gnosok gnay nad , ria tapme iges ayaiB .
i amatrep pahat isakola kutnu natukgnagnep : in
062.3 = )91(04 + )01(01 + )02(06 + )5(04 + )02(05 = CT
lebaT 5 .tuaL taraB tuduS namodeP nagneD lawA pahaT isakolA .7.
eK
iraD gnaduG
A gnaduG
B gnaduG
C satisapaK
kirbaP
W kirbaP
02
5
8
09
H kirbaP
51
02
01
06
P kirbaP
52
01
91
05
nahutubeK
gnaduG
05
011
04
002
.c rorrE dna lairT araceS isakolA habugneM
lebaT adap isakola ,natukgnagnep ayaib ignarugnem kutnU 5 habuid 7.
araces rorre dna lairt .
akam ,isiret muleb AH tapme iges ,A gnaduG molok adap aynlasiM
apme iges irad nahadnimep nagned )not( nautas 1 isiid abocid gnay t
laH .05 patet gnadug nahutubek raga AW tapme iges irad aynlasim ,nial
itrepes BH nad BW tapme iges ihuragnepmem naka aguj utnet ini
halada naktabikaid gnay ayaib nahabureP .8.6 lebaT adap tahilret
:tukireb iagabes
ayaib nahabmaT : A ek H irad 1 = 5 B ek W irad 5 = 02
ayaib nagnarugneP : A ek W irad 02 = B ek H irad = 02 04
ada itrareb ,04 ayaib nagnarugnep gnades 02 ayaib nahabmaT
02 natamehgnep )not 1( tinu 1 isakol nahadnimep paites kutnu )000.02 pR=(
,ini naataynek nakrasdreB .BH nad AW irad BW nad AH tapme iges ek gnarab
,)ajas tinu 1 aynah kadit( kaynab hibel nakanaskalid gnay isakola halmuj alib
halmuJ .kaynab hibel naka aynnatamehgnep akam mumiskam habuid asib
rasebes takedret gnay tapme iges 2 irad licekret isi .isiid naka gnay nagned
.06 = BH tapme iges isi irad licek hibel ,05 = AW tapme iges isi ini lah malaD
tapme iges isi alup nakhabmatid nad tinu 05 AH tapme iges adap nakisiid idaJ
BW ini isakola nahabureP .tinu 05 rasebes )AH nagned gnakaleb kalotreb gnay(
05 04
06
01 04
natukgnagnep ayaib naklisahgnem nagned ,9.6 lebaT adap tahilret itrepes
.harum hibel gnay
lebaT 5 .rorrE dna lairT nagned amatreP nakiabreP .8. eK
iraD gnaduG
A gnaduG
B gnaduG
C satisapaK
kirbaP
W kirbaP
02 05
(- )
5 04
)+(
8
09
H kirbaP
51
)+(
02 06
(-)
01
06
P kirbaP
52
01 01
91 04
05
nahutubeK
gnaduG
05
011
04
002
lebaT 5 .rorrE dna lairT nagned audeK nakiabreP .9.
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
irbaP W k
02 05
5 04 09
8
09
H kirbaP
51 05
02 06 01
01
06
P kirbaP
52
01 01
91 04
05
nahutubeK
gnaduG
05
011
04
002
)02(01 + )51(05 + )5(09 = CT 062.2 = )91(04 + )01(01 + irad harum hibel
lebaT( amatrep isakola 5 .)7.
bugnem nagned nakukalid aguj tapad ini isakola nahabureP isakola ha
,CW tapme iges isiid naka ,aynlasiM .natakedreb kadit gnay tapme iges adap
nad ,BP ,BW tapme iges apureb tapad habureb tuki gnay nial tapme iges akam
lebaT adap tahilret itrepes CP 5 .01.
lebaT 5 uajreB tapmE igeS nagned isakolA nakiabreP .01. .nah
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
W kirbaP
02
5 09 05
8 04
09
H kirbaP
51 05
02 01
01
06
P kirbaP
52
01 01 05
91 04
05
nahutubeK
gnaduG
05
011
04
002
1(05 + )02(01 + )51(05 + )8(04 + )5(05 = CT 020.2 = )0
nahaburep nagned alib nahaburep nakadaid aynsuretes halnaikimeD
natukgnagnep ayaib helorepid aynrihka iapmas ,ayaib ignarugnem tapad uti
.)lamitpo( hadneret gnay
lebaT 5 .rorrE dna lairT nagned agiteK nakiabreP .11. eK
iraD G gnadu
A gnaduG
B gnaduG
C satisapaK
kirbaP
W kirbaP
02
5 05 06
8 04 03
09
H kirbaP
51 05
02 01
01 01
06
P kirbaP
52
01 05
91
05
nahutubeK
gnaduG
05
011
04
002
lebaT 5 .rorrE dna lairT nagned lamitpO isuloS .21.
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
W kirbaP
02
5 06
8 03
09
H kirbaP
51 05
02
01 01
06
P kirbaP
52
01 05
91
05
nahutubeK
gnaduG
05
011
04
002
: uata , lamitpo isatropsnart ayaib latot akaM
5 + )51(05 + )8(03 + )5(06 = CT 005 + 001 + 057 + 042 + 003 = )01(0
.098.1 =
.2.3.5 )noitubirtsiD deifidoM( IDOM edoteM
gnippetS edotem irad isakifidom nakapurem IDOM edoteM - .enotS
malad anerak tamrec hibel gnay lamitpo lisah helorepmem tapad ini edoteM
sok tapme iges nakutnenem nagned nakukalid ayaib tamehgnem asib gnay gno
hakgnal nupadA .tapet nad itsap hibel gnay rudesorp - ayngnutihgnem hakgnal
:tukireb iagabes halada
hawaB nanaK ek satA iriK tuduS irad amatreP lebaT halisI
lebaT 5 duS namodeP nagneD lawA pahaT isakolA .7. taraB tu .tuaL
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
W kirbaP
02
5
8
09
H kirbaP
51
02
01
06
P kirbaP
52
01
91
05
nahutubeK
gnaduG
05
011
04
002
05 04
06
01 04
moloK nad siraB ialiN nakutneneM
naamasrep nakrasadreb nakutnetid molok nad sirab ialiN jiC = jK + iR .
siraB sirab ialin nad ,0 ialin irebid ulales amatrep - molok nad sirab - nial molok
lisah nakrasadreb nakutnetid - .helorepid gnay nagnutihrep lisah
sirab ialiN R = W W .0 = :A molok ialin iracneM
RW K + A C = AW K + 0 A K= A molok ialin ,02 = A 02 =
ok ialin iracneM nial gnay sirab nad mol RW K + B C = BW K + 0 ; B K ; 5 = B 5 = RH K + B C = BH R ; H R ; 02 = 5 + H 51 = RP K + B C = BP R ; H R ; 01 = 5 + P 5 = RP K + C C = CP K + 5 ; C K ; 91 = C 41 =
ialiN - gnay molok/sirab adap nakkatelid naidumek ini ialin
lebaT adap tahilret itrepes ,natukgnasreb 5 .31.
lebaT 5 .moloK nad siraB ialiN naisigneP .31. eK
iraD gnaduG
02 = A gnaduG
5 = B gnaduG
41= C satisapaK
kirbaP
kirbaP 0 = W
02
5
8
09
kirbaP
51 = H
51
02
01
06
kirbaP
5 = P
52
01
91
05
nahutubeK
gnaduG
05
011
04
002
nI gnutihgneM nakiabreP sked
gnay tapme iges( ria tapme iges irad ialin halada nakiabrep skednI
:sumur nagned ayniracneM .)gnosok
C ji – Ri - Kj nakiabrep skedni =
lebaT 5 nakiabreP skednI gnutihgneM .41.
tapmE igeS
C ji - Rj - Kj
nakiabreP skednI
AH AP CW CH
51 - 51 - 02 52 - 5 - 02 8 - 0 - 41
01 - 51 - 41
- 02 0
- 6 - 91
05 04
06
01 04
nahabureP kaloT kitiT hilimeM
irebid alib itrareb fitagen nakiabrep skedni iaynupmem gnay tapme igeS
p ayaib halmuj ignarugnem tapad naka )isiid( isakola aliB .natukgnagne
ayaib nakianek nakbabeynem naka naisignep itrareb fitisop aynialin
iges halada nahaburep kalot kitit nakapurem gnay tapme igeS .natukgnagnep
aynskedni gnay tapme rasebret aynakgna nad fitagen adnatreb malaD .
emem gnay ataynret ,41.6 lebaT anerak helO .AH tapme iges halada tarays ihun
.isiid naka gnay tapme iges iagabes hilipid ini tapme iges uti
isakolA ikiabrepmeM
iges 1 halhiliP .)AH( hilipret gnay tapme iges adap fitisop adnat halireB
me iges 1 ,)BH( sirabes nad takedret isi gnay tapme nad takedret isi gnay tap
halhilip naidumeK .ini tapme iges 2 adap fitagen adnat halireB .)AW( molokes
adnatreb gnay tapme iges 2 nagned molokes uata sirabes gnay tapme iges utas
ayntujnaleS .fitisop adnat ini tapme iges halireb nad ,)BW( idat fitagen
dnip adnatreb gnay ek fitagen adnatreb gnay tapme iges irad isakola halnakha
iges idaJ .)05( fitisop adnatreb gnay tapme iges irad licekret isi kaynabes fitisop
06 isireb BH tapme iges ,05 isireb naidumek AH tapme - tapme iges ,01 = 05
d ,09 = 05 + 04 isireb BW lebaT tahiL( isireb kadit idajnem AW tapme iges na
5 .)51.
lebaT 5 isakolA helorepmeM kutnu isakolA nahabureP .51.
.IDOM edoteM nagned lamitpO
eK iraD
gnaduG 02 = A
gnaduG 5 = B
gnaduG 41 = C
satisapaK kirbaP
kirbaP
0 = W
02 05
(- )
5 04 09
)+(
8
09
kirbaP
51 = H
51 05
)+(
02 06 01 (-)
01
06
kirbaP
5 = P
52
01 01
91 04
05
nahutubeK
gnaduG
05
011
04
002
lebaT 5 helorepmeM kutnU amatreP isakolA nahabureP .61.
.IDOM edoteM nagned lamitpO isakolA
eK D ira
gnaduG 02 = A
gnaduG 5 = B
gnaduG 41 = C
satisapaK kirbaP
kirbaP
0 = W
02
5 09
8
09
kirbaP
51 = H
51 05
02 01
01
06
kirbaP
5 = P
52
01 01
91 04
05
nahutubeK
gnaduG
05
011
04
002
)91( 04 + )01( 01 + )02( 01 + )51( 05 + )5( 09 = isatropsnart ayaiB
062.2 =
hakgnaL halgnalU - sataiD tubesreT hakgnaL
aliB .hadneret ayaib helorepid iapmas audek romon hakgnal ialuM
tubesret isakola itrareb fitagen ialinreb gnay nakiabrep skedni ada hisam
kadit hadus aliB .natukgnagnep ayaib ignarugnem kutnu habuid tapad hisam
ada nahaburep hotnoc iagabeS .lamitpo hadus itrareb fitagen gnay skedni
lebaT adap tahilid tapad lamitpo lebat iapacnem iapmas amatrep 5 ,71. 5 ,81.
nad 5 .91.
lebaT 5 helorepmeM kutnu audeK isakolA nahabureP .71. mitpO isakolA .IDOM edoteM nagned la
eK iraD
gnaduG 0 = A
gnaduG 5 = B
gnaduG 41 = C
satisapaK kirbaP
kirbaP
0 = W
02
5 09
8
09
kirbaP
51 = H
51 05
02 01
(- )
01 01 )+(
06
kirbaP
5 = P
52
01 01 02
)+(
91 04 03 (- )
05
nahutubeK
gnaduG
05
011
04
002
atropsnart ayaiB 070.2 = )91(03 + )01(02 + )01(01 + )51(05 + )5(09 = is
lebaT 5 helorepmeM kutnU agiteK isakolA nahabureP .81.
.IDOM edoteM nagned lamitpO isakolA eK
iraD gnaduG
91 = A gnaduG
5 = B gnaduG
41 = C satisapaK
kirbaP
kirbaP 0 = W
02
5 09 06
(- )
8 03
)+(
09
kirbaP
= H - 4
51 05
02
01 01
06
kirbaP
5 = P
52
01 02 05
)+(
91 03
(- )
05
nahutubeK
gnaduG
05
011
04
002
098.1 = )01(05 + )01(01 + )51(05 + )8(03 + )5(06 = isatropsnart ayaiB
lebaT 5 isakolA helorepmeM kutnU isakolA nahabureP .91.
IDOM edoteM nagned lamitpO eK
iraD gnaduG
31 = A gnaduG
5 = B gnaduG
8 = C satisapaK
kirbaP
kirbaP 0 = W
02
5 06
8 03
09
kirbaP
2 = H
51 05
02
01 01
06
kirbaP
5 = P
52
01 05
91
05
nahutubeK gnaduG
05
011
04
002
lebaT 5 adap nakiabrep skedni anerak igal naklamitpoid asib kadit 91.
paites ria tapme iges lebaT adap tahilret itrepes ,fitagen gnay ada kadit hadus
5 .02.
lebaT 5 lebaT nakiabreP skednI .02. 5 91.
tapmE igeS
C ji - Rj - Kj
nakiabreP skednI
AW BH AP CP
02 - 0 - 31 02 - 2 - 5 52 - 5 - 31 91 - 5 - 8
7 31 7 6
.3.3.5 noitamixorppA s’legoV edoteM
V edoteM nakapurem )MAV( dohteM noitamixorppA s’legoV uata lego
irad isakola rutagnem tapad kutnu tapec hibel nad hadum hibel gnay edotem
hakgnal nupadA .narasamep haread aparebeb ek rebmus aparebeb - hakgnal
:tukireb iagabes halada ayngnutihgnem kutnu
.a tubek halnusuS gnisam satisapak ,nahu - ayaib nad ,rebmus gnisam
lebaT adap itrepes kirtam malad ek natukgnagnep 5 .6.
lebaT 5 isatropsnarT lebaT .6. eK
iraD gnaduG
A gnaduG
B gnaduG
C satisapaK
kirbaP
kirbaP W
02 X 11
5 X 21
8 X 31
09
kirbaP
H
51 X 12
02 X 22
01 X 32
06
kirbaP
P
52 X 13
01 X 23
91 X 33
05
nahutubeK gnaduG
05
011
04
2 00
.b ayaib utiay ,)tulosba ialin malad( licekret ayaib aud irad naadebrep haliraC
C( skirtam adap molok nad sirab pait kutnu audek licekret nad licekret ji .)
gnay irad aud romon nad 5 = licekret tukgna ayaib W sirab adap aynlasiM
ab ialin idaJ .8 = licekret 8 = W sir - ialin aynsuretes naikimeD .3 = 5 - ialin
:tukireb iagabes nial gnay
H siraB 51 = - 5 = 01 P siraB 91 = - 9 = 01 A moloK 02 = - 5 = 51 B moloK 01 = - 5 = 5
C moloK 01 = - 2 = 8
.c naadebrep ialin 1 halhiliP - na id rasebret gnay naadebrep ialin aumes arat
ialin iaynupmem P sirab ini lah malaD .sirab nad molok adap naadebrep
.9 utiay ,rasebret naadebrep
.d sirab uata molok malad kusamret gnay tapme iges utas halas adap halisI
gnay tapme iges adap utiay ,hilipret hadneret aynayaib iges aratnaid
asib gnay nikgnum kaynabes aynnaisI .uti sirab/molok adap nial tapme
,52 = AP tapme iges kutnu tukgna ayaib ,P sirab adap aynlasiM .nakukalid
ayaib halada licekret gnaY .91 = CP tapme iges nad ,01 = BP tapme iges
pme iges isi atik akaM .BP tapme iges adap hibel( nautas 05 nagned BP ta
.)05 = P kirbap satisapak anerak nikgnum kadit nautas 05 irad
lebaT 5 aluM noituloS elbisaeF .12. - edoteM irad alum .noitamixorppA s’legoV
kirbap amaN gnaduG
C B A ebreP naad
sirab satisapaK W
H kirbaP P
8 5 02 01 02 51 91 01 52
3 09 5 06 9 05
nahutubeK molok naadebreP
04 011 05 2 5 5
X nahiliP BP 05 = P sirab nakgnaliH
.e satisapak( aynhunepes isiid hadus tubesret sirab anerak P sirab nakgnaliH
nad molok nakitahrep naidumeK .igal isiid nikgnum kadit aggnihes )hunep
leb gnay sirab .)C ,B ,A molok nad ,H ,W sirab( isakolaret/isiret mu
.f ek hakgnal adap ayaib )hisiles( naadebrep ilabmek nakutneT - kutnu 2
hakgnal nagned iapmas 3 hakgnal gnalU .isiret muleb gnay sirab nad molok
tahil( isakolaret aynhunepes molok nad sirab aumes iapmas ,5 lebaT 5 .)22.
lebaT 5 .natujnaL MAV irad noituloS elbisaeF .22.
kirbap amaN gnaduG
C B A naadebreP
sirab satisapaK W
kirbaP H
02 8 5 01 02 51
3 09 5 06
nahutubeK molok naadebreP
04 06 05 2 51 5
X nahiliP BW 06 = B molok nakgnaliH
kirbap amaN
gnaduG A C
naadebreP sirab satisapaK
W kirbaP
H
8 02 01 51
21 03 5 06
nahutubeK molok naadebreP
04 05 2 5
X nahiliP CW 03 = W sirab nakgnaliH
kirbap amaN
gnaduG C A
satisapaK
H kirbaP 51 01 06 nahutubeK
01 05
X nahiliP AH 05 = X CH 01 =
halada sataid noitamixorppA s’legoV edotem nagned isakola kirtam ,idaJ
:tukireb iagabes
lebaT 5 edoteM nagned isakolA lisaH skirtaM .32. .MAV
eK iraD
gnaduG A
gnaduG B
gnaduG C
satisapaK kirbaP
kirbaP
W
02
5 06
8 03
09
kirbaP
H
51 05
02
01 01
06
kirbaP
P
52
01 05
91
05
nahutubeK gnaduG
05
011
04
002
.g rayabid surah gnay aynisatropsnart ayaib akam ,aumes isiret haleteS
098.1 = )01( 05 + )01( 01 + )51( 05 + )8( 03 + )5( 06 :halada
.h aliB utas gnay lasim ,amas aynraseb gnay 2 ada ayaib naadebrep ialin
molok maladek kusam gnay tapme iges haltahil akam molok adap katelret
ini tapme iges aliB .rasebret ialin iaynupmem gnay sirab nupuam
ta sirab adap tapme iges aratnaid hadneret ayaib iaynupmem ,aynmolok ua
kadit aynayaib aliB .ini tapme iges adap mumiskam isakola nakisi akam
,utas halas rasadreb isiid naka gnay tapme iges halhilip akam ,hadneret
.e nad d hakgnal adap itrepes ,hilipret molok uata hilipret sirab
.1 nahitaL
nagnem naahasurep haubeS haread agit ek lasa toped agit irad alug tukg
ek toped pait irad tukgna sokgno nakrabmaggnem ini tukireb lebaT .naujut
gnisam - toped pait id aidesret gnay alug halmuj aguj nad naujut tapmet gnisam
.haread pait nahutubek atres
natukgnA ataD .1.1 lebaT eK
iraD hareaD
T1 hareaD
T2 hareaD
T3
namirigneP
topeD A1
05 021
001
001
021
topeD
A2
002 03
003 041
002
071
topeD
A3
001
002 07
003 09
061
nahutubeK
051
012
09
054
:naaynatreP
edotem nakanuggnem nagned lamitpo isatropsnart ayaib halgnutiH
.MAV nad ,idoM ,enotS gnippetS
5 gnabmieS kaT isatropsnarT halasaM .4.
igab adaP ,gnabmies isatropsnart halasam sahabid halet ini mulebes na
nakaynabek ,aynranebeS .naatnimrep nagned amas narawanep halmuj anamid
hibel narawanep halmuj anamid gnabmies kat halada isatropsnart halasam
sam susak malaD .aynkilabes uata naatnimrep irad raseb ,gnabmies kat hala
.isakifidom tikides nakhutubmem isatropsnart isulos edotem
narawaneP irad raseB hibeL naatnimreP
gnabmies kat halasam isulos imahamem nakhadumem kutnU
:tukireb hotnoc nakitahrep ,ini )narawanep > naatnimrep(
reb aragen naahasurep haubeS agit irad kupup tukgnagnem nagnitnepek
agitek adap naatnimrep ,kirbap agitek ylppus satisapaK .rasap agit ek kirbap
:tukireb iagabes halada tinu rep isatropsnart ayaib nad rasap
naatnimreP
narawaneP
D1
D2
D3
narawaneP
S1
S2
S3
8
51
3
5
01
9
6
21
01
021
08
08
naatnimreP
051
07
09
082 013
: tukireb iagabes naksumurid tapad sataid halasaM
X8 = Z .niM 11 X5+ 21 X6+ 31 X5+ 12 X01+ 22 X21+ 32 X3+ 13 X9+ 23 X01+ 33
X :tarays nagneD 11 X + 21 X + 31 021 =
X 12 X + 22 X + 32 08 =
X 13 X + 23 X + 33 051 =
X 11 X + 12 X + 13 ≤ 051
X 21 X + 22 X + 23 ≤ 07
X 31 X + 32 X + 33 ≤ 07
X aumeS ji ≥ 0
( naamaskaditeK ≤ aumes awhab nakkujnunem naatnimrep aladnek )
aladnek hibel uata utas numan ,nakmirikid naka aidesret gnay tinu
id ulrep ,uti kutnU .ihunepret naka kat naatnimrep sirab utaus nakhabmat
adap nakkujnutid isakifidomid gnay lebaT .isatropsnart lebat malad ymmud
.2 lebat
aggnihes nakhabmatid halet )nalayahk ylppus/rebmus( ymmud utauS
kutnu tinu rep ropnart ayaiB .naatnimrep nad narawanep nakgnabmieynem
lada naujut agitek katok ek isakola anerak lon ha - kadit uti katok
lebarav nagned golana ini ymmud katoK .aynhuggnuses isulos ihuragnepmem
.lon nagned amas naujut isgnuf malad aynisubirtnok ialin gnay ,kcals
naktapadnem kutnu edotem ihuragnepmem kadit ymmud nahabmaneP
isulos edotem nagned mumitpo isulos nakutnenem edotem nupuam lawa
htroN edoteM .MAV nad IDOM ,enotS gnippetS - ini susak malad renroC tseW
,IDOM nad enotS gnippetS edotem malaD .nahaburep imalagnem kadit aguj
katok - katok itrepes nakukalrepid ymmud katok - gnay katok malaD .nial
C ialin ,MAV edotem ji akitek hadneret molok ayaib iagabes nakanugid ymmud
.tsoc ytinutroppo nagnutihrep nakukalid
lebaT .5 24 ) S > D ( isakifidomiD gnaY isatropsnarT lebaT .
naatnimreP narawaneP
D1
D2
D3
narawaneP
S1
8
5
6
021
S2
51
01
21
08
S3
3
9
01
08
ymmuD
0 0 0 03
naatnimreP
051
07
09
013
.A ENOTS GNIPPETS EDOTEM
lebaT 52.5 tuaL taraB tuduS edoteM lawA isakolA . naatnimreP
narawaneP
D1
D2
D3
narawaneP
S1
8 021
5
6
021
S2
51 03
01 05
21
08
S3
3
9 02
01 06
08
ymmuD
0 0 0 03
03
naatnimreP
051
07
09
013
)lawa isakola( isatropsnart ayaib latoT
)0 x 03( + )01 x 06( + )9 x 02( + )01 x 05( + )51 x 03( + )8 x 021( = CT 0 + 006 + 081 + 005 + 054 + 069 = 096.2 =
lebaT 62.5 amatreP nakiabreP .
naatnimreP narawaneP
D1
D2
D3
narawaneP
S1
8 021
5
6
021
S2
51 03 01
(- )
01 05 07
)+(
21
08
S3
3 02
)+(
9 02
(-)
01 06
08
ymmuD
0 0 0 03
03
naatnimreP
051
07
09
013
rep( isatropsnart ayaib latoT )amatrep nakiab
)0 x 03( + )01 x 06( + )3 x 02( + )01 x 07( + )51 x 01( + )8 x 021( = CT 0 + 006 + 06 + 007 + 051 + 069 = 074.2 =
5 lebaT 72. audeK nakiabreP .
naatnimreP narawaneP
D1
D2
D3
narawaneP
S1
8 021 06
5
6 06
021
S2
51 01
01 07
21
08
S3
3 02 08
9
01 06
08
ymmuD
0 0 0 03
03
naatnimreP
051
07
09
013
)audek nakiabrep( isatropsnart ayaib latoT
( + )3 x 08( + )01 x 07( + )51 x 01( + )6 x 06( + )8 x 06( = CT )0 x 03 0 + 042 + 007 + 051 + 063 + 084 = 039.1 =
lebaT 82.5 agiteK nakiabreP .
naatnimreP
narawaneP
D1
D2
D3
narawaneP
S1
8 06 07
5
6 06 05
021
S2
51 01
01 07
21 01
08
S3
3 08
9
01
08
ymmuD
0 0 0 03
03
naatnimreP
051
07
09
013
)agitek nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )3 x 08( + )21 x 01( + )01 x 07( + )6 x 05( + )8 x 07( = CT 0 + 042 + 021 + 007 + 003 + 065 = 029.1 =
lebaT 92.5 tapmeeK nakiabreP .
naatnimreP
narawaneP
D1
D2
D3
narawaneP
S1
8 07 04
5
6 05 08
021
S2
51
01 07
21 01
08
S3
3 08
9
01
08
ymmuD
0 03
0 0 03
03
naatnimreP
051
07
09
013
)agitek nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )3 x 08( + )21 x 01( + )01 x 07( + )6 x 08( + )8 x 04( = CT 0 + 042 + 021 + 007 + 084 + 023 = 068.1 =
lebaT 03.5 mumitpO isakolA .
naatnimreP narawaneP
D1
D2
D3
narawaneP
S1
8 04
5
6 08
021
S2
51
01 07
21 01
08
S3
3 08
9
01
08
ymmuD
0 03
0 0
03
naatnimreP
051
07
09
013
068.1 = lamitpo isatropsnart ayaib latoT
IDOM EDOTEM
lebaT .5 31 tuaL taraB tuduS edoteM lawA isakolA .
naatnimreP arawaneP n
D1
D2
D3
narawaneP
S1
8 021
5
6
021
S2
51 03
01 05
21
08
S3
3
9 02
01 06
08
ymmuD
0 0 0 03
03
naatnimreP
051
07
09
013
molok ialin nad sirab ialin nakutneneM
R 1S 0 = nautneteK
R 1S K + 1D C = 1D1S R 3S K + 2D C = 2D3S
K + 0 1D K 8 = 1D R 8 = 3S R 9 = 3 + 3S 6 =
R 2S K + 1D C = 1D2S R 3S K + 3D C = 3D3S R 2S R 51 = 8 + 2S K + 6 7 = D3 K 01 = 3D 4 =
R 2S K + 2D C = 2D2S R uD K + 3D C = 3DUD
K + 7 2D K 01 = 2D R 3 = uD R 0 = 4 + UD = - 4
lebaT 23.5 moloK ialiN nad siraB ialiN naisigneP . naatnimreP narawaneP
D1 8 =
D 2 3 =
D 3 4 =
narawaneP
S1 0 =
8 021
5
6
021
S2 7 =
51 03
01 05
21
08
S3 = 6
3
9 02
01 06
08
= muD - 4
0 0 0 03
03
naatnimreP
051
07
09
013
.5 lebaT .33 nakiabreP skednI gnutihgneM
tapmE igeS
C ji – Ri - Kj
nakiabreP skednI
S1D2 S1D3
S2D3
S3D1
DUD1
DUD2
5 – 0 – 3 6 – 0 – 4
21 – 7 – 4 3 – 6 – 8 0 – (- )4 – 8 0 – (- )4 – 3
2 2 1
- 11 √ - 4
1
lebaT 43.5 lamitpO isakolA helorepmeM kutnU isakolA nahabureP .)1 nakiabreP(
naatnimreP narawaneP
D1 8 =
D 2 3 =
D 3 4 =
narawaneP
S1 0 =
8 021
5
6
021
S2 7 =
51 03 01
01 05 07
21
08
S3 6 =
3 02
9 02
01 06
08
= muD - 4
0 0 0 03
03
naatnimreP
051
07
09
013
)1 nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )01 x 06( + )3 x 02( + )01 x 07( + )51 x 01( + )8 x 021( = CT 0 + 006 + 06 + 007 + 051 + 069 = 074.2 =
utneneM molok ialin nad sirab ialin nak
R 1S 0 = nautneteK R 1S K + 1D C = 1D1S R 2S K + 2D C = 2D2S
K + 0 1D K 8 = 1D K + 7 8 = 2D K 01 = 2D 3 =
R 2S K + 1D C = 1D2S R 3S K + 3D C = 3D3S R 2S R 51 = 8 + 2S 7 = - K + 5 3D K 01 = 3D 51 =
R 3S K + 1D C = 1D3S R uD K + 3D C = 3DUD R 3S R 3 = 8 + 3S = - 5 R uD R 0 = 51 + UD = - 51
lebaT 53.5 nakiabreP skednI gnutihgneM .
tapmE igeS
C ji – Ri - Kj
nakiabreP skednI
S1D2 S1D3
S2D3
S3D2
DUD1
DUD2
5 – 0 – 3 6 – 0 – 51
21 – 7 – 51 9 – (- )5 – 3
0 – (- )51 – 8 0 – (- )51 – 3
2 - 9 - 01 √ 11 7
21
lebaT 53.5 isakolA helorepmeM kutnU isakolA nahabureP . )2 nakiabreP( lamitpO
naatnimreP narawaneP
D1 8 =
D 2 3 =
D 3 4 =
narawaneP
S1 0 =
8 021
5
6
021
S2 7 =
51 01
01 07
21 01
08
S3 = - 5
3 02 03
9
01 06 05
08
muD = - 51
0 0 0 03
03
naatnimreP
051
07
09
013
)2 nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )01 x 05( + )3 x 03( + )21 x 01( + )01 x 07( + )8 x 021( = CT 05 + 09 + 021 + 007 + 069 = 0 + 0 073.2 =
molok ialin nad sirab ialin nakutneneM
R 1S 0 = nautneteK R 1S K + 1D C = 1D1S R 2S K + 3D C = 3D2S
K + 0 1D K 8 = 1D R 8 = 2S R 21 = 51 + 2S = - 3
R 3S K + 1D C = 1D3S R 2S K + 2D C = 2D2S R 3S R 3 = 8 + 3S = - 5 - K + 3 2D K 01 = 2D 31 =
R 3S K + 3D C = 3D3S R uD K + 3D C = 3DUD - 5 K + 3D K 01 = 3D R 51 = uD R 0 = 51 + UD = - 51
lebaT 63.5 nakiabreP skednI gnutihgneM .
tapmE igeS
C ji – Ri - Kj
nakiabreP skednI
S1D2 S1D3
S2D1
S3D2
DUD1
DUD2
5 – 0 – 31 6 – 0 – 51
51 – (- )3 – 8 9 – (- )5 – 31 0 – (- )51 – 8 0 – (- )51 – 31
- 8 - 9 √
01 1 7 2
lebaT 73.5 isakolA helorepmeM kutnU isakolA nahabureP . )3 nakiabreP( lamitpO
naatnimreP narawaneP
D1 8 =
D 2 31 =
D 3 51 =
narawaneP
S1 0 =
8 021 07
5
6 05
021
S2 = - 3
51
01 07
21 01
08
S3 = - 5
3 03 08
9
01 05
08
= muD - 51
0 0 0 03
03
naatnimreP
051
07
09
013
)3 nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )03 x 08( + )21 x 01( + )01 x 07( + )6 x 05( + )8 x 07( = CT = 0 + 042 + 021 + 007 + 003 + 065 029.1 =
molok ialin nad sirab ialin nakutneneM R 1S 0 = nautneteK
R 1S K + 1D C = 1D1S R 2S K + 2D C = 2D2S
K + 0 1D 8 = K 1D 8 = K + 6 2D 01 = K 2D 4 =
R 1S K + 3D C = 3D1S R 3S K + 1D C = 1D3S K + 0 3D K 6 = 3D R 6 = 3S R 3 = 8 + 3S = - 5
R 2S K + 3D C = 3D2S R uD + K 3D C = 3DUD R 2S R 21 = 6 + 2S R 6 = uD R 0 = 6 + UD = - 6
lebaT 83.5 nakiabreP skednI gnutihgneM .
tapmE igeS
C ji – Ri - Kj
nakiabreP skednI
S1D2 S2D1
S3D2
DUD1
DUD2
5 – 0 – 4 51 – 6 – 8 9 – ( - )5 – 4 0 – ( - )6 – 8 0 – ( - )6 – 4
1 1
01 - 2 √
2
lebaT 93.5 isakolA helorepmeM kutnU isakolA nahabureP . )4 nakiabreP( lamitpO
naatnimreP narawaneP
D1 8 =
D 2 4 =
D 3 6 =
narawaneP
S1 0 =
8 07 04
5
6 05 08
021
S2 6 =
51
01 07
21 01
08
S3 = - 5
3 08
9
01
08
= muD - 51
0 03
0 0 03
03
naatnimreP
051
07
09
013
)4 nakiabrep( isatropsnart ayaib latoT
)0 x 03( + )3 x 08( + )21 x 01( + )01 x 07( + )6 x 08( + )8 x 04( = CT 0 + 042 + 021 + 007 + 084 + 023 = 068.1 =
tneneM molok ialin nad sirab ialin naku R 1S 0 = nautneteK
R 1S K + 1D C = 1D1S R 2S K + 2D C = 2D2S
K + 0 1D K 8 = 1D K + 6 8 = 2D K 01 = 2D 4 =
R 1S K + 3D C = 3D1S R 3S K + 1D C = 1D3S K + 0 3D K 6 = 3D R 6 = 3S R 3 = 8 + 3S = - 5
R 2S K + 3D C = 3D2S R uD K + 3D C = 3DUD R 2S R 21 = 6 + 2S R 6 = uD R 0 = 8 + UD = - 8
lebaT 04.5 nakiabreP skednI gnutihgneM .
tapmE igeS
C ji – Ri - Kj
nakiabreP skednI
S1D2 S2D1
S3D2
S3D3
DUD2
DUD3
5 – 0 – 4 51 – 6 – 8 9 – ( - 5 ) – 4
01 – )5 ( – 6 0 – ( - )8 – 4 0 – ( - )8 – 6
1 1
01 9 4 2
lebaT 14.5 isakolA helorepmeM kutnU isakolA nahabureP . )4 nakiabreP( lamitpO
naatnimreP narawaneP
D1 8 =
D 2 4 =
D 3 6 =
narawaneP
S1 0 =
8 04
5
6 08
021
S2 6 =
51
01 07
21 01
08
S3 = - 5
3 08
9
01
08
= muD - 8
0 03
0 0
03
naatnimreP
051
07
09
013
t ayaib latoT 068.1 = lamitpo isatropsnar
)MAV( EDOTEM NOITAMIXORPPA S’LEGOV .C
lebaT 24.5 aluM noituloS elbisaeF . - legoV edoteM irad aluM
naatnimreP narawaneP
D 1 D2 D3
naadebreP siraB narawaneP
S1
S2 S3
Du
6 5 8 21 01 51 01 9 3 0 0 0
1 021 2 08
08 6 0 03
naatnimreP moloK naadebreP
09 07 051 4 4 5
S nahiliP 3D 1 08 = S siraB nakgnaliH 3
lebaT 4.5 audeK pahaT noituloS elbisaeF .2
naatnimreP narawaneP
D 1 D2 D3
naadebreP siraB narawaneP
S1 S2 Du
6 5 8 21 01 51 0 0 0
1 021 2 08 0 03
naatnimreP moloK naadebreP
09 07 07 6 5 7
liP D nahi uD 1 03 = D siraB nakgnaliH u
lebaT 4.5 agiteK pahaT noituloS elbisaeF .3
naatnimreP narawaneP
D 1 D2 D3
naadebreP siraB narawaneP
S1 S2
5 8 6 21 01 51
1 021 2 08
naatnimreP moloK naadebreP
09 07 04 6 5 7
S nahiliP 1D 1 04 = D moloK nakgnaliH 1
lebaT 4.5 tapmeeK pahaT noituloS elbisaeF .4
naatnimreP narawaneP
D2 D3
naadebreP siraB narawaneP
S1 S2
6 5 21 01
1 08 2 08
naatnimreP moloK naadebreP
09 07 6 5
S nahiliP 1D 3 08 = S siraB nakgnaliH 1
lebaT 4.5 amileK pahaT noituloS elbisaeF .5
naatnimreP narawaneP
D2 D3
narawaneP
S2 21 01 08
naatnimreP
01 07
S nahiliP 2D 2 07 = S2D 3 01 =
lebaT 4.5 teM lamitpO isakolA skirtaM .6 legoV edo naatnimreP
narawaneP
D1
D 2
D 3
narawaneP
S1
8 04
5
6 08
021
S2
51
01 07
21 01
08
S3
3 08
9
01
08
uD
0 03
0 0
03
naatnimreP
051
07
09
013
:uata lamitpo isatropsnart ayaib latoT
8 x 04( = CT )0 x 03( + )3 x 08( + )21 x 01( + )01 x 07( + )6 x 08( + ) 0 + 042 + 021 + 007 + 084 + 023 = 068.1 =