Intro Algebraico

 

Omtrdkuffoöm Ao Aolm lmvl vlmo mokd kd c tu tuss cp cpum umtl tlss kl klbb slh slhum umkd kd tr troj ojls lstr trl, l, lb da danl nlto tovd vd kl lstd lstdss cp cpum umtl tlss ls kc kcrt rtl l um umc c elrrcjolmtc kl lstukod y rlpcsd kl bd yc vostd lm fbcsl. Qlfulrkc qul sl rlquolrl kl tu lstukod plrsdmcb pcrc bdhrcr bc tdtcb fdjprlmsoöm kl bds fdmflptds y tljcs yc cmcbozckds.

Bc jltc lm lstc pcrtl klb fursd ls>

Qlsdbvlr prdabljcs jlkocmtl bc `drjubcfoöm y sdbufoöm cbhlarcofc kl lfucfodmls bomlcbls kl bc  `drjc Cx + A : F   y Cx + A : Fx + K Kdmkl C,A,F y K sdm mþjlrds fdmdfokds qul plrtlmlflm c bds mþjlrds rlcbls, ls klfor klfor,, qul pulklm slr mþjlrds mcturcbls, lmtlrds, rcfodmcbls d orrcfodmcbls. _, pcrc lmtrcr lm jctlroc, cadrkcrljds fdmflptds aãsofds qul tl slrãm kl jufec utobokck lm bc tcrlc kl cprlmklr c rlsdbvlr prdabljcs j jlkocmtl lkocmtl lfucfodmls kl projlr hrckd. Vl rlquolrl qul fdjprlmkcs fdjprlmkcs fckc fdmflpt fdmflptd d lxpulstd y qul trct trctls ls kl rlsdbvlr [DKDV _ FCKC \MD kl bds lnlrfofods fdm tdkc bc jcbc omtlmsoöm kl cprlmklr!!!  Cb `omcb kl fckc tljc lmfdmtrcrãs um plqulód cpcrtckd fdm um rlsujlm kl bds fdmflptds hlmlrcbls utobozckds lm lb josjd. Md kukls lm lxpdmlr tus kukcs pcrc bds fdmflptds y lnlrfofods qul bcs hlmlrlm c tu prd`lsdr prd`lsdr.. [cjaoïm sl cmlxc c lstl kdfujlmtd um cpcrtckd kl mdtcs y lnlrfofods kl rlpcsd kl bds tljcs ojpdrtcmtls qul sl rlquolrlm pcrc lstl pcrfocb vostds lm lb pcrfocb pcsckd. Ycrc ls lsttc pcrtl rtl klb fu furs rsd d kla lalr lrã ãs yc fdmdflr y pdklr tr trc cacncr ncr fdm> •

•

•

  Dplrcfodmls Aãsofcs   Fcmtokckls fdm sohmd   Ydtlmfocs.

[l rlfdjolmkd qul so tolmls prdabljcs fdm cbhumd kl lsds tljcs tl rl`olrcs cb cmlxd kl mdtcs y lnlrfofods kl rlpcsd .

Jufed ïxotd y tl klsld lb jlndr kl bds cprlmkozcnls!! 

3

 

‒Fdmflptds Yrlbojomcrls‚   Crotjïtofc> Ycrtl kl bc jctljãtofc qul lstukoc bds mþjlrds y bcs dplrcfodmls qul sl ecflm fdm lbbds Ycrtl l kl bcs b cs jctljãtofcs qul trctc kl bc fcmtokck lm  Ãbhlarc> Ycrt hlmlrcb, rlprlslmtãmkdbc rlprlslmtãmkdbc pdr jlkod kl bltrcs u dtrds sohmds. Lm fursds cmtlrodrls kl jctljãtofcs cprlmkostl bd qul lm jctljãtofcs sl fdmdfl fdjd crotjïtofc, ls klf klfor or,, trcac trcacncs ncstl tl fd fdm m mþj mþjlr lrds ds y rlc rlcboz bozcst cstl l dpl dplrc rcfod fodmls mls aãs aãsofc ofcss fdm lbb lbbds ds (su (sujcs jcs,, rls rlstc tcs, s, jubtopbofcfodmls y kovosodmls fdm mþjlrds lmtlrds, rcfomdcbls y mþjlrds klfojcbls. Lm lstc pcrtl klb fursd ecrljds cbhd um pdfd ko`lrlmtl, cedrc, ckljãs kl bds mþjlrds y bcs dplrcfodmls qul sl pulklm rlcbozcr fdm lbbds,  omtrdkuforljds bltrcs y sêjadbds qul rlprlslmtcm

fcmtokckls (mþjlrds!) kl bds qul sl ecabc kl jcmlrc hlmlrcb pdrqul md tolmlm um vcbdr `ond d md fdmdfljds su vcbdr vcbdr..

1

 

‒Bc jubtopbofcfoöm lm lb Ãbhlarc‚  Bcs dplrcfodmls aãsofcs (sujc, rlstc, jubtopbofcfoöm y kovosoöm) sohulm solmkd prãftofcjlmtl bcs josjcs y su böhofc md fcjaoc kl momhumc jcmlrc. Bd qul so fcjaoc kl jcmlrc ojpdrtcmtl ls bc mdtcfoöm kl bc jubtopbofcfoöm y lb slmtokd qul tdjc lb prdkuftd (rlsubtckd kl bc jubtopbofcfoöm) cb trcacncr fcmtokckls fdm sohmd. Lm hlmlrcb, y fdjd sl jlmfodmö lm fbcsl sl pulkl rlprlslmtcr umc jubtopbofcfoöm kl bcs sohuolmtls jcmlrcs>

 :  ∘  : () ()(() _ bcs trls sohmo`ofcm bd josjd> Bc jubtopbofcfoöm ö prdkuftd kl ―  x‟ y ― y‟ 

Qlfulrkc qul, lmtrl kds fcmtokckls, so md sl cfbcrc so lstãm sujcmkd, rlst lstcmkd, d kovoko okolmk lmkd   VOLJYQ VOLJYQLL sl

fdmsoklrc qul lstãm jubtopbofcmkd!!! 

‒Bc lxprlsoöm cbhlarcofc aãsofc‚  Lb projlr pcsd yc lstã kckd y cedrc mds `cbtc fdmsoklrcr fdmsoklrcr bc tlrjomdbdhêc qul lstc lstcrljds rljds utobozcmk utobozcmkd d lm lb mtd ãbhlarc bcs lfucfodmls kl tofds bc ds jcmlrc jcslxpr jêmojcjlmtl klfor, mlflsotcjds umb fdmnu fd mnumt d kl yfd fdmfl mflpt ptds ds jct jctljã ljãtof aãs aãsof ofds, ds, lx prlsc lsckds kds kl mlflscroc, bc `drjc `drjc ls jcs mct mctur urcb cb y fd fdbdq bdquoc uocb pdsoabl pcrc qul ecabljds lb josjd okodjc. Ycrc Yc rc lbbd lbbd tl pr prls lslm lmtd td um umc c lxpr lxprls lsoöm oöm cb cbhl hlar arco cofc fc jc jcss slmf slmfob obbc bc y hl hlml mlrrcb qu qul l sl fd fdmd mdfl fl fd fdjd jd

jdmdjod.

 

 

Lxpdmlmtl Pcrocabl, botlrcb, d omföhmotc

Fdl`ofolmtl

6

 

 Cmcbofljds cedrc fckc pcrtl, su fdmflpt fdmflptd d y sohmo`ofckd.

Pcrocabl, botlrcb d omf öhmotc>   Vêjadbd qul rlprlslmtc lb vcbdr d vcbdrls vcbdr ls qul pulkl tdjcr umc kltlrjomckc jchmotuk.   

  Ls um mþjlrd d mþjlrds kltrãs kl um sêjadbd    Cb omof omofod od klb prdabljc md fdmdfljds fdmdfljds su vcbdr vcbdr y bd trctcrljds fdjd fucbquolr mþjlrd

x>

Fdl`ofolmtl> Mþjlrd qul sl lsfroal c bc ozquolrkc kl umc vcrocabl, botlrcb d omföhmotc y qul omkofc lb mþjlrd kl vlfls qul lstl klal jubtopbofcrsl.

c>



Ls um mþjlrd qul plrtlmlfl cb fdmnumtd kl bds mþjlrds



rlcbls pdr bd qul pulkl slr mcturcb, lmtlrd, rcfodmcb d orrcfodmcb. Fucmkd vcbl 3, MD sl lsfroal Jubtopbofc c bc vcrocabl. Lm lfucfodmls, soljprl scaljds fucmtd vcbl.

 

Lxpdmlmtl>

Mþjlrd qul  omkofc fucmtcs vlfls ec kl jubtopbofcrsl umc vcrocabl pdr so josjc (fucmkd (fucmkd m=3). Lm hlmlrcb hlmlrcb omkofc c qul pdtlmfoc klal lblvcrsl lb vcbdr kl x  

m>

  

Ls um mþjlrd qul plrtl rtlmlfl cb fdmnum numtd kl bds mþjlrds rlcbls pdr bd qul pulkl slr mcturcb, lmtlrd, rcfodmcb d orrcfodmcb. Fucmkd vcbl 3, MD sl lsfr lsfroa oal l Omkofc fucmtcs vlfls ec kl jubtopbofcrsl pdr so josjc umc vcr vcroca ocabl fucm fucmk kd ls um mþj mþjlrd lrd mcturc turcbb. Lm bcs lfucfodmls, lb hrckd kl bc lfucfoöm sl fdmsohul tdjcmkd lm fulmtc lb tïrjomd fdm lxpdmlmtl jcs hrcmkl.

;

 

[ïrjomds cbhlarcofds y fdmstcmtls. ãbhlarc rc,, um tïrjo tïrjomd md ls lb lb pr prdkuf dkuftd td kl um um [ïrjomd cbhlarcofd>   Lm ãbhla `cftdr mujïrofd (Fdl`ofolmtl) pdr umc d jãs vcrocabls. Lm fckc  tïrjomd  cbhlarcofd sl kostomhulm lb fdl`ofolmtl mujïrofd (qul omfbuyl lb sohmd y fdmstcmtls jctljãtofcs) y bc pcrtl botlrcb (qul omfbuyl vcrocabls).

[ïrjomd fdmstcmtl>  \m tïrjomd fdmstcmtl d umc fdmstcmtl ls um lbljlmtd kl umc lxprlsoöm cbhlarcofc qul md fcjaoc su vcbdr. vcbdr. Kofed kl dtrc jcmlrc sdm bds tïrjomds qul md lstãm jubtopbofckds pdr momhumc vcrocabl.

Lnljpbds Obustrctovds> 3.- Ok Oklm lmto` to`oqu oqul l fd fdl`o l`ofol folmt mtls, ls, vcroc vcrocabl abls, s, lx lxpdm pdmlm lmtl tlss y fd fdmst mstcm cmtl tlss lm bcs soh sohuol uolmt mtls ls lxprlsodmls cbhlarcofcs.

6    + 31 ; x, Lxpdmlmtl>1, Fdmstcmtl> 31 



Fdl`ofolmtl> , Pcrocabl> w, Lxpdmlmtl Lxpdmlmtl>> 6, Fdmstcmtl> 3 

Fdl`ofolmtl>6, Pcrocabl> j, Lxpdmlmtl> 1, Fdmstcmtl> 9

Fdl`ofolmtl>3 y, Lxpdmlmtl> 3, Fdmstcmtl> 8

Fdl`ofolmtl>3, Pcrocabl> t, Lxpdmlmtl> 3, Fdmstcmtl> -39

<

 

3.- Ok Oklm lmto` to`oqu oqul l fd fdl`o l`ofol folmt mtls, ls, vcroc vcrocabl abls, s, lx lxpdm pdmlm lmtls tls y fd fdmst mstcm cmtl tlss lm bcs soh sohuol uolmt mtls ls lxprlsodmls cbhlarcofcs.

6    + 31 ;



Fdl`ofolmtl> , Pcrocabl> x, Lxpdmlmtl>1, Fdmstcmtl> 31 



w, Lxpdmlmtl Lxpdmlmtl>> 6, Fdmstcmtl> 3 

Fdl`ofolmtl>6, Pcrocabl> j, Lxpdmlmtl> 1, Fdmstcmtl> 9

Fdl`ofolmtl>3 y, Lxpdmlmtl> 3, Fdmstcmtl> 8

Fdl`ofolmtl>3, Pcrocabl> t, Lxpdmlmtl> 3, Fdmstcmtl> -39

0