GFPI-F-135 - Guia 2293957 Algebra de Matrices DIAM

 

 

XRLMI]L FI GI]VCÝ@ FI JLRKDMCÝ@ XRLJI]CL@DA C@VIGRDA JLRKDVL GYËD FI DXRI@FC_DOI

CFI@VCJCMDMCÝ@ FI AD GYCD FI DXRI@FC_DOI



 

 







Fi`lkc`dm Fi`lkc `dmcý` cý` fia Xrlgrd Xrlgrdkd kd fi Jlrkdm Jlrkdmcý` cý`??  Vim` Vim`ýa ýalg lgl l i` Fcsiô Fcsiôl l fi C` C`ti tigr grdm dmcý cý` ` fi  Dutlkdtcskls Kimdtrl`cmls Mýfcgl fia Xrlgrdkd fi Jlrkdmcý`? 22=247 Z488. JCMND ]LJCD XAY]? 2=2=697 @lkbri fia Xrlyimtl?  Fcsiôl fi u` scstikd fi ml`trla kifcd`ti pam pdrd lpirdr ad pad`td fi c`struki`tdmcý` y ml`trla fi prlmisls c`fustrcdais i` ia si`d MCKC GCRÝ@ ]d`td`fir. Jdsi fia Xrlyimtl? D`äacscs Dmtcvcfdf fi Xrlyimtl? Fisdrrlaadr ndbcacfdfis i` ia kd`iol fi scstikds fi imudmcl`is ac`idais (].I.A)5 pdrd djcd`zdr ml`lmckci`tls tim`laýgcmls i` dpacmdmcl`is c`fustrcdais mlkl? Aiy fi Ecrmnnljj (@lfls y Kdaads). Ijimtu tudr dr kifcm kifcmcl cl`is `is fi supi supirj rjcm cmcis cis y ml`t ml`tlr lr`l `lss fi dmui dmuirf rfl l ml` ml` pad`ls pad`ls y Mlkpiti`mcd?  Ijim ispimcjcmdmcl`is tãm`cmds Risuatdfls fi Dpri`fczdoi Damd`zdr?  Dpacmdr ml`miptls y lpirdmcl`is qui si riadmcl`i` ml`? aýgcmd aýgc md kdtik kdtikätc ätcmd, md, gilki gilkitrë trëd, d, trc trcgl` gl`lki lkitrë trëd, d, i` ia fisdrr fisdrrlaal laal fi ads ju`mcl ju`mcl`is `is prlpcds prlpcds fi su lmupdmcý` Furdmcý` fi ad Guëd? 6 Nlrds (4 siscý` fi 6 nlrds).

2. XRI]I@VDMCÝ@ Isti flmuki Isti flmuki`tl `tl ml`tci`i ml`tci`i ad guëd guëd prämtc prämtcmd md fi dagibr dagibrd d fi kdtrcm kdtrcmis, is, sus lpirdm lpirdmcl` cl`is? is? sukd, sukd, ristd ristd y kuatcpacmdmc kuatc pacmdmcý` ý` l prlfumtl, prlfumtl, dfikäs, dfikäs, fi u` kãtlfl kãtlfl pdrd rislavir scstikds scstikds fi imudmcl`is ac`idais? ac`idais? (2x2), (2x2), (=x=), (6x=), (6x6)5 plr ad tãm`cmd fi bdscjcmdmcý` (Bdsi), qui ndmi pdrti fi ad mlkpiti`mcd fi kdtikätcmds qui si ckpdrti d als tim`ýalgls fi Fcsiôl i C`tigrdmcý` C`tigrdmcý` fi Dutlkdtcskls Dutlkdtcskls Kimdtrl`c Kimdtrl`cmls, mls, i` ia ]I@D ” MCKC 5 Gcrý` - ]d`td`fir, dpacmd`fl ad pifdglgëd `uistrd ad muda, si bdsd i` ia ml`strumtcvcskl i` ia duad y dpacmd u`d sirci fi pdsls aýgcmls pdrd ia fisdrrlaal fi mlkpiti`mcds bäscmds i` ia dpri`fcz. Als lboitcvls fi istd guëd sl`? 



Ridaczdr ioirmcmcls fi sukd, ristd y kuatcpacmdmcý` fi kdtrcmis, dfikäs, fi fdr d ml`lmir ad tãm`cmd fi bdscjcmdmcý`, pdrd rislavir scstikds fi imudmcl`is ac`idais, dpacmdfds i` isti mdsl d ad tim`lalgëd i` Kimdtrl`cmd, Iaãmtrl`cmd, Kimd`cmd. Ivcfi`mcdr ad ioimumcý` fi tdrids ispimëjcmds, riadmcl`dfds ml` ad tim`lalgëd i` Kd`ti`ckci`tl Iaimtrlkimä Iaimtr lkimä`cml `cml C`fustrcda C`fustrcda,, i` u` prlmisl prlmisl rida, dpacmd`fl als ml`lmckci`t ml`lmckci`tls ls tiýrcml-pr tiýrcml-prämtcm ämtcmls ls ml`strucfls i` ia dkbci`ti fi jlrkdmcý` (Zcrtuda).

GJXC-J-4=9 Z84

 

 

I]VCKDFL] DXRI@FCMI]?  Als c`vctl d mlkprlkiti mlkprlkitirsi rsi i` su prlpcl prlmisl prlmisl jlrkdtcvl jlrkdtcvl ml` kcrds d fisdrrlaadr fisdrrlaadr ads mlkpiti`mc mlkpiti`mcds ds riquircfds plr ia simtlr prlfumtcvl pdrd u` tim`ýalgl i` Dutlkdtczdmcý` C`fustrcda, i` bi`ijcmcl prlpcl y fi ad slmcifdf.

=. JLRKYADMCÝ@ FI AD] DMVCZCFDFI] FI DXRI@FC_DOI DXRI@FC_DOI Y`d kdtrcz is u`d tdbad bcfcki`scl`da fi `ÿkirls i` md`tcfdfis dbstrdmtds qui puifi` sukdrsi y kuatcpacmdrsi. Fi ltrd kd`ird käs si`mcaad, is u` drrigal l fcsplscmcý` fi `ÿkirls l sëkblals, fcspuistls i` jcads y mlauk`ds. Ads kdtrcmis si utcaczd` pdrd fismrcbcr scstikds fi imudmcl`is ac`idais, y rigcstrdr als fdtls qui fipi`fi` fi vdrcls pdräkitrls. Ads lpirdmcl`is ml` kdtrcmis sl` ad sukd, ad ristd y ad kuatcpacmdmcý`. @l ixcsti u`d fijc`cm fij c`cmcý` cý` pdrd pdrd ad fcv fcvcsc cscý` ý` fi kdtrc kdtrcmis mis Ad fcv fcvcscý cscý` ` fi kdtrcm kdtrcmis is `l istä istä privcd privcdki` ki`ti ti fitirk fitirkc`d c`dfd. fd. Vãm`cmdki`ti `l ixcsti ad fcvcscý` fi kdtrcmis. Fcvcfcr u`d kdtrcz i`tri ltrd is u`d ju`mcý` c`fijc`cfd. Ia iqucvdai`ti käs mirmd`l is kuatcpacmdr plr ad c`virsd fi ltrd kdtrcz I` ad vcfd fcdrcd fcdrcd ia ml`mip ml`miptl tl fi kdtrc kdtrcmis mis is fi grd` grd` riaivd riaivd`mc `mcd, d, yd qui ads kdtrc kdtrcmis mis si usd` usd` mlkl mlkl ml`ti`iflris pdrd dakdmi`dr fdtls riadmcl`dfls.  Dmtudaki`ti, ads kdtrcmis sl` fi kumnd utcacfdf i` prlbaikds prämtcmls fi ad vcfd fcdrcd. ]lbri tlfl, i` dquiaals qui c`vlaumrd` ]cstikds fi Imudmcl`is Ac`idais. Ad ridaczdmcý` fi ad kdtrcz mlkl nirrdkci`td fi trdbdol, jdmcactd ia mukpackci`tl fia trdbdol fi`trl fi u`d ikprisd, mlkl pdrti fi ad rivcscý` pdrd ivcfi`mcdr sc si istä` dpacmd`fl y mukpaci`fl als riqucsctls. I` ad dmtudacfdf ads ikprisds fi tlfl tcpl y `cvia istä` mdfd viz käs c`tirisdfds i` mirtcjcmdrsi i` mdacfdf y istl `l si puifi ndmir sc istds tris `lrkds `l vd` fi ad kd`l, fi dnë ad ckplrtd`mcd fi ad ridaczdmcý` fi isti trdbdol. Ads tris `lrkds si c`tigrd` fi tda jlrkd qui su dpacmdmcý`, aaivd d ads lrgd`czdmcl`is d mukpacr  ml` tlfls als riqucsctls `imisdrcls pdrd sir mirtcjcmdfds.

Dpacmdmcý` fi ads Kdtrcmis i` ads fcjiri`tis Vim`lalgëds? ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌

Rislavir mcrmuctls iaãmtrcmls. Rislavir scstikds fi imudmcl`is. I`mrcptdr mýfcgls. (]igurcfdf C`jlrkätcmd)  D`daczdr prlbdbcacfdfis fi mlrriflris fi blasd blasd (Ji`ýki`l Daidtlrcl).  Dakdmi`dkci`tl fi c`jlrkdmcý` lptckd lptckd i` scstikds (Bdsis fi Fdtls).  Dyufd pdrd grdjcmdr ju`mcl`is mruzdfds. Vrdbdodr ads kdtrcmis fi Kärelv (Kdtrcz fi Xrlbdbcacfdf).  D`daczdr rifis iaãmtrcmds.  D`daczdr mrimckci`tl fi plbadmcl`is. (Bdsis (Bdsis fi Fdtls) Ridaczdr kdtrcz fi cfi`tcjcmdmcý` y vdalrdmcý` fi piacgrls y rcisgls. Ridaczdr kdtrcz fi dspimtls gi`irdais i ckpdmtls dkbci`tdais.

Rislavir u` scstikd fi imudmcl`is ac`idais is i`ml`trdr tlfds sus slaumcl`is

GJXC-J-4=9 Z84

 

 

Vãm`cmd fi Bdscjcmdmcý`? Is u` kãtlfl qui busmd kiolrdr ad jlrkd fi rislavir scstikds fi imudmcl`is ac`idais, ml` kcrds d jlrtdaimir, ia fisdrrlaal `ukãrcml fi ads vdrcdbais prisi`tis i` mdfd u`d fi ads imudmcl`is. ]i utcaczd u`d slad jlrkuad y u`ls pdräkitrls qui jdmcactd` ad dpacmdmcý` fi isti kãtlfl. Jlrkuad?  Xrlfumtl  Xrl fumtl fi ad Fcdgl`da Fcdgl`da − Xr  Xrlfumtl lfumtl fi ad Fcdgl`da fia Xcvlti ]imu`fdrcd ]imu`fdrcd

Virkc`l d I`ml`trdr

¼

¼

 Xcvlti

 

¼

Xdräkitrls? 





Xdsdr ia scstikd fi imudmcl`is ac`idais fi jlrkd kdtrcmcda d ad jlrkd fi ad cfã`tcmd dmlkpdôdfd fi ad mlauk`d fi ads vdrcdbais l c`mýg`ctds Ia `ÿkirl fi imudmcl`is i c`mýg`ctds (=x=)5 fibi sir fi cguda lrfi` da fi ad cfã`tcmd? (=x=)5 pirl i` jcads y mlauk`ds Ia kãtlfl fi Bdscjcmdmcý` is jaixcbai pdrd siaimmcl`dr ia pcvlti5 scikpri y mud`fl, sid fcjiri`ti fi ‑mirl‛.



Ia Xcvlti fibi sir fcjiri`ti fi ‑Mirl‛5 pirl, puifi sir i`tirl + ¼l−¼, jrdmmcl`drcl l fimckda.



Ia pcvlti si mlkpl`i fi u`d jcad pcvltda y u`d mlauk`d pcvltda.









Y`d viz nimnl ia pcvlti, ‑u`l‛, i` ad `uivd kdtrcz, als fikäs iaiki`tls fi ad mlauk`d pcvltda si ml`vcirti` i` ‑mirl‛. ]c i` ad jcad pcvltda ndy iaiki`tls ‑mirl‛, als fikäs iaiki`tls fi ad mlauk`d, ml auk`d, pirkd`imi` cgudais. Istd tãm`cmd si bdsd i` ad Kdtrcz Cfã`tcmd (Kdtrcz Mudfrdfd qui plsii iaiki`tls ‑u`l‛ i` su fcdgl`da prc`mcpda y als fikäs iaiki`tls sl` ‑mirls‛).

( )

  Kdtrcz Cfi`tcmd ? C ;

4

8

8

8

4

8

8

8

4

 

=  x =

GJXC-J-4=9 Z84

 

 



]c ia scstikd fi imudmcl`is ac`idais is fi? = x =  (tris imudmcl`is ml` tris c`mýg`ctds), da pdsdral da kãtlfl fi bdscjcmdmcl`5 plr su puistl, mdfd cgudafdf, iqucvdai d u` `ÿkirl fdfl, al qui gi`ird u` scstikd fi? = x 6, qui da ml`jrl`tdral ml` ad tãm`cmd risuatd? Z 4 + ¼ Z 2 + ¼ Z =;¼ 2



= Z 4−¼ ¼ 2 Z 2−¼ Z =;¼ 6  −2 Z 4 + ¼ Z 2 + ¼ 2 Z  =;¼ 2

 4  

4

4

=   −2   −4 −2 4 2

(

4

8

8

  Z 4

  8

4 8

8 4

  Z 2     Z =

2 6 2

) (  

8

)

Riqucsctls pdrd ridaczdr ad Guëd fi Dpri`fczdoi? 



Ia tëtual tëtual fia c`jlrki c`jlrki is? Dpiaacfls\@lk Dpiaacfls\@lkbris\ bris\Kdtik Kdtikätcmds ätcmds.pfj. .pfj. Ioikpal? Ioikpal? Blaëvdr Blaëvdr Xãriz\ Xifrl\   Dsmd`cl.Kdtikätcmds.pfj  ]ctcl wib i`trigd flmuki`tl? Ia c`jlrki si fibi subcr d ad padtdjlrkd GLLGAI FRCZI, d trdvãs fia mlrril? Kcsi`d.

@LVD 4. ]c prisi`td` c`ml`vi`ci`t c`ml`vi`ci`tis is i` ia Gllgai frcvi, i`vcdr c`jlrki da c`strumtlr c`strumtlr??  oork>>Hkcsi`  oork>>Hkcsi`d.ifu.ml d.ifu.ml  /  rnlrfuzHkcsi`d.i rnlrfuz Hkcsi`d.ifu.ml fu.ml

@LVD 2. I` ia mdsl fi qui ad dmtcvcfdf fi dpri`fczdoi sid ridaczdfd i` jlrkdtl fcgctda5 als pdräkitrls d utcaczdr sl`? Muirpl Muirp l fia flmuki`tl flmuki`tl Wlrf? kë`ckl kë`ckl 2 pägc`ds pägc`ds l ads qui si riquciri`, riquciri`, ml` tdkdôl tdkdôl fi aitrd aitrd Drcda 42, C`tirac`idfl si`mcaal y dpacmd`fl `lrkds CML@VIM pdrd prisi`tdr trdbdols ismrctls. I` al plscbai c`sirtdr ckägi`is, tdbads, imudmcl`is y ac`es (i`admis YRA) d vcfils, ml` ia jc` fi i`rcquimir  ia c`jlrki c`jlrki.. @l lavcfdr rijiri`mcdr l mlpcdr YRA l fcrimmcý` WIB  pdrd juturds ml`suatds fi fcmnds ckägi`is l tdbads. @l is `imisdrcl subcr als vcfils da GLLGAI FRCZI, pirl sc fdr = ml`mauscl`is fia vcfil lbsirvdfl.

IOIRMCMCL] D FI]DRRLAADR? Ia dpri`fcz fi dmuirfl ml` mdfd mdfd u`l fi als ioirmcmcls prisi`tdf prisi`tdfls ls fibi istdr pripdrdfl pdrd pdrd djcd`zdr als ml`lmckci`tls tãm`cmls tãm`cmls i` ia tikd fi Dagibrd Kdtrcmcda, Kdtrcmcda, y, sus lpirdmcl`is, dfikäs fi u` kãtlfl kãtlfl pdrd rislavir scstikds fi imudmcl`is ac`idais. Xdrd iaal prlpl`ikls ad tãm`cmd fi bdscjcmdmcý`. 4     

2 Z4  + Z2 + Z =  ; = 2 Z4  + = Z2  + Z= ; 6 Z4  - Z2  - 2 Z=  ; - 9

2-

Z 4  Z 2  Z =  2Z4 

=-

Z4  + Z2 + Z=  ; = 2 Z4  - Z2  - = Z= ; - 2

6-

C 4  C 4 

+ C2  + C=  ; 3 + C2  + C6 ; 48 

C 4 

+ C=  + C6  ; 44

6 Z4  - Z2  - = Z=  ; 8

- Z 2  + Z=   + 2 Z 6  - = Z6 

; -: ; = ; 6 ; 9

GJXC-J-4=9 Z84

 

 

C 2  9 

Z4  + Z2  + Z= 2Z4  - Z2  - = Z=  Z4  - Z2  - Z=  6 Z4  - Z2  - = Z= 

; = ; - 2 ; - 4 ; 8

:-

9 Z4  + 2 Z2  - Z= 2Z4  + =Z2  + 6 Z=  =Z4  + 6Z2  + 2 Z= 

; = ; - 4 ; >

>-

 

7 

3 

-2 Z4  - =Z4  Z 4 

+ =Z2  - Z=  ; -9 + Z2  - 2Z=  ; -42 + 2 Z2  - =Z=  ; -4

+ C=  + C6  ; 42

>8 C 4  - 68 C2  - 28 C=  ; 38 - 68 C 4  + >8 C2  - 28 C=  ; =8 -28 C 4  + 28 C2  + >8 C=  ; 8

C 4  6C 4  - C 4    = C4 

+ =C2  - C=  + C 2  - 2C=  +  =C6 + 9 C2  + =C= - C6 + 2 C2  + C= + C6

48 -

-2 C 4  C 4  2C4  - C 4 

 

+ + + +

=C2  C=  C2  C= 

; 2 ; 6 ; 4 ;-2

+ 2C=  ; -4 - 2C6  ; = - C6  ; 2 - 6 C6  ; 8

44- Fdfl ia ].I.A? = x =5 rislaviral y i`ml`trdr i `ml`trdr ia vdalr fi ad c`mýg`ctd ‑K‛. Z 4+ ¼ Z 2− ¼ Z =;¼ 28

 2 Z 4−¼ Z 2 + ¼ 2 Z = ;¼ K  Z 4+ ¼ Z 2+ ¼ Z = ;¼ 4: 42- Fdfl? ]cstikd ]cstikd fi Imudmcl`is Ac`idais? Ac`idais? 6 x 6. I`ml`trdr ia vdalr fi ad cc`mýg`ctd `mýg`ctd ‑K‛5 sc als fdtls sl sl`? `? Als risuatdfls fia ].I.A5 privcdki`ti fisdrrlaadfls, sc` ti`ir i` mui`td ia vdalr fi ad c`mýg`ctd ‑K‛ gi`irl als risuatdfls scguci`tis? Z 4;=4 Z 2;=7 Z =;−=6 Z 6 ;43

Dkbci`ti Riquircfl? Vrdbdol i` Mdsd (Jlrkdmcý` Zcrtuda).

Kdtircdais  

Xrisi`tdmcl`is ridaczdfds plr ia prljislr. Zcfils dscg`dfls plr ia c`strumtlr c `strumtlr GJXC-J-4=9 Z84

 

 

      

Xrisi`tdmcý` fi Nirrdkci`tds C`jlrkätcmds Guëd fi Dpri`fczdoi Mudfir`l fi Dpu`tis Rigads (Ismudfrds y Vrd`splrtdflris) Blacgrdjls, Adpcz, Blrrdflr  Mdamuadflrd Mci`tcjcmd (]ckuadflr Fcgctda) XM, Fcsplsctcvl Klvca, C`tir`it

6. DMVCZCFDFI] FI IZDAYDMCÝ@

Ivcfi`mcds fi fi Dp Dpri`fczdoi

Mrctircls fi fi Iv Ivdaudmcý`

Ivcfi`mcd Ivcfi` mcdss fi Ml`lmc Ml`lmckci kci`tl `tl? 4- Ridaczd ad lpirdmcý` d klfls aýgcml ml y gräj gräjcm cml, l, ad ti tik kät ätcm cmd d Aimturd c`cmcda ” slaumcý` aýgc pad`tidfd, sigÿ` riquirckci`tl prigu`tds. fia prlbaikd i` ml`tixtl. Ivcfi`mcds fi Xrlfumtl? I`t I`trig rigd ia fi fissdr drrrla laal al fi ad adss dmtcvcf dmt cvcfdfi dfiss fi ju`fdk ju`fdki`t i`tdmc dmcý` ý` slbri slb ri ad dpacmd dpacmdmcý mcý` ` fia Dagibr Dagibrd d Kdtrcmcda i` sctudmcl`is fi ml`tixtl rida, dpacmd`fl ad tãm`cmd fi Bdscjcmdmcý` (BD]I).

Vãm`cmds i C`struki`tls fi fi Ivdaudmcý` I`trigdr ia risuatdfl fi ads  Dmtcvcfdfis fi Dpri`fczdoi d fisdrrlaadr, i` u` c`jlrki jc`da d tr trdvãs dvãs fi ad padtdj padtdjlrk lrkd d Gllgai Gllgai Frcvi kcsi`d.

2- Riml`lmi c`jlrkdmcý` td`tl mud`t mud`tctctdt dtcv cvd d y mudac mudactd tdtctcvd vd,, fi dmuirf dmu irfl l d al sukc`cs sukc`cstrd trdfl fl i` u` u`d d sctud ctudmc mcý` ý` fi ml` l`ti tixt xtl l pdrtcmuadr d pdrtcr fi ad tikätcmd fi rislaumcý` fi ]cstikds fi Imudmc Imu dmcl`i l`iss Ac`ida Ac`idais is (].I.A (].I.A), ), ml mlkl kl al is ad dpac dpacmd mdmc mcý` ý` i` tim`lalgëd iaãmtrcmd.

9. GAL]DRCL FI VÃRKC@L] Jdvlr rivcsdr i` ad wib, ads scguci`tis fijc`cmcl`is l tãrkc`ls?

42=6-

Im Imu udm dmccý` ý`,, ]cs ]cstik tikd d fi Im Imudmc udmcl`is l`is Ac`i Ac`idai dais, s, Kdtrcz, Lp Lpir irdmc dmcl` l`is is Bä Bäsc scmds mds,,

9Ia iki`t i`tls ls d Kd Kdtr trcz cz,, :- Iaik Jcad Jcad Xc Xcvl vltd tda,a,fi aad GJXC-J-4=9 Z84

 

 

7- Ml Mlau auk` k`d d Xc Xcvl vltd tda,a, >- Xcvlti, 3- Kd Kdtr trcz cz Mu Mudfr dfrdf dfd, d, 48-Kdtrcz Rimtd`guadr, 44-Kdtrcz Cfã`tcmd, 42-Kdtrcz @uad, 4=-Zimtlr Jcad, 46-Zimtlr Mlauk`d, 49-Jýrkuad pdrd mdamuadr ia Xcvlti, 4:-Ristrcmmcl`is 47-]laumcý` fia ]cstikd fi Imudmcl`is Ac`idais 4>-Lrfi` fi ad Kdtrcz.

:. RIJIRI@VI] BCABCLGRÄJCML]         

nttps?// nttps?//www.ylu www.ylutubi.ml tubi.mlk/wdtmn k/wdtmn