Algebra_Lineal_y_sus_Aplicaciones.jb.decrypted.pdf

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Îio`dtn ice`ni s vpv nzicfnfcke`v ] @ T F @ T N @ M C F C Ö E N F ] PN PN I C X N M N

Mwm F Is Pew`tv}s k Atsiem ‖ Fkiiò` Ztb

]TNMPFFCÖE H`vøv @i`t Aptt`} Aptt`}





























































































































INS) MNWCM F% ÎIO@DTN ICE@NI S VPV NZICFNFCKE@V Z@NTVKE @MPFNFCÖE) Aãfk) 4::? CVDE8 3?
Zîoev8 0<=

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N ac `vzkvn) Iciicne) s n ep`v}tnv lchnv Fltcv}cen) M`dktnl s Aìcvvn) fpsk nzksk) îecakv) s ﬎ì`v ktnfcke`v lcfc`tke zkvcdi` `v}` icdtk





























































































































Nf`tfn mì np}kt

Mwm F Is }è` ikv }á}pikv m` D N m` Nptkt Pew`tv}s ,Ciiekv#) s m` A N s ZL M zkt i Pew`tvmm m` Fikte è Ikv Îeoì`v @i ztk`vkt Is l vmk f}`! mtî}fk ` ew`v}omkt è }`î}fv m`vm` 377) ztefziè}` è i i  Pew`tvmm m` Atsiem) Fkiiò` Ztb ]dãe l }tdhmk fkk ztk`vkt wv}e}` è i Pew`tv! mm m` Îv}`tm) è i Pew`tvmm Idt` m` Îv}`tm s è i Pew`tvmm m` B! v`tvip}`te) Ni`e ]è` ]è` îv m` }t`e} t}áfpikv m` ew`v}oföe ew`v}oföe zpdifmkv fkk eîivv pefkei s îio`dt ie`i Fkk `dtk pemmkt mì Otpzk m` @v}pmk mì Fpttáfpip m` Îio`dt Ie`i z}tkfemk zkt i EVG) ì ztk`vkt Is l vmk iám`t è ì kwè}k f}pi zt km`text ì zie m` `v}pmkv m` îio`dt ie`i @i ztk`vkt Is }dãe `v fkp}kt m` wtkv }`}kv }`î}fkv) è}t` ìikv) Ce}tkmpf}cke }k Gpef}ckeni Nenisvcv ) fke Neopv @ ]sikt) Fnifpipv nem c}v Nzzicfn}ckev ) fke I H Okimv}`e s M C Vfle`m`t) s Ice`nt Nio`dtn Oèv ‖ Nvv`}v kt Pem`totnmpn}` Pem`totnmpn}` An}làn}cfv ) fke M Ftivke) F T Hklevke s N M Zkt}`t F}`mtî}fk m` zt`t iáe` @i ztk`vkt Is l t`fdmk fp}tk zt`kv pew`t! v}tkv zkt `fìèf mkfè}`) efipmk è 337 ì m` Mv}eopvl`m Vflkit‖]`! fl`t m` i Pew`tvmm m` Atsiem @e 33=) v` i` fkef`mö pek m` ikv Zt`kv m` i A}l`}fi Nvvkf}ke k N`tf) ~p` ii`w ì }á}pik m` Mv}eopvl`m Fkiiò` kt Pew`tv}s ]`fleo ]`fleo k A}l`}fv L vmk ìòmk zkt ikv `v}pme}`v pew`tv}tkv `dtk m` i Nizl Idm Mì} E}kei Vflkiv}f Lkekt Vkf`}s s m` i Okimè B`s E}kei Lkekt Vkf`}s @e 3<3) i Nptkt Pew`tv}s i` fkef`mö ì zt`k Kp}v}emeo Kp}v}eme o Nipepv @i mkf}kt Is `v `dtk m` i N`tfe A}l`}fi Vkf`}s)





























































































































Fke}ècmk Zt`fk c| Ek} zt ikv `v}pme}`v FNZÁ]PIK

>

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@fpnfcke`v ice`ni`v è îio`dtn ice`ni @H@AZIK CE]TKMPF]KTCK8

` ceoèc`tán  4 6 = 0 7 ? < 3 :

FNZÁ]PIK

4

>

Akmìkv ice`ni`v è `fkekaán

>

Vv}`v m` `fpfke`v ie`i`v 4 T`mpfföe zkt giv s ktv `vfikemv >= @fpfke`v w`f}kti`v 4< I `fpföe }tfi N| 1 d =: Fkehpe}kv vkipföe m` ikv vv}`v ie`i`v 0: Nziffke`v m` ikv vv}`v ie`i`v 0? Cem`zèmèf ie`i 70 Ce}tkmpfföe  iv }tevktfke`v ie`i`v ?6 I }tx m` pe }tevktföe ie`i <4 Akmìkv ie`i`v è eòkfkv) fèfv ` eoè`tá @h`tffkv vpzi`è}tkv >:4

34

Îio`dtn m` an}tcf`v >:0 @H@AZIK CE]TKMPF]KTCK8

m` nwcke`v

>:0

Akmìkv m` fkazp}nmktn è ì mcv`þk































































































































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Fke}ècmk

FNZÁ]PIK

6

M`}`tacene}`v

><0

@H@AZIK CE]TKMPF]KTCK8

6 64 66

FNZÁ]PIK

=

Ce}tkmpfföe  ikv m`}`tee}`v ><7 Ztkz`mm`v m` ikv m`}`tee}`v >34 Tòi m` Ft`t) wkipè s }tevktfke`v ie`i`v @h`tffkv vpzi`è}tkv 4>>

@vznfckv w`f}ktcni`v @H@AZIK CE]TKMPF]KTCK8

= =4 =6 == =0 =7 =? =< =3

M`}`tacene}`v è o`ka`}tán neniá}cfn

><0

4:>

4>0 Wpìk `vznfcni s vcv}ànv m` fke}tki

@vzfkv s vpd`vzfkv w`f}kti`v 4>7 @vzfkv epikv) `vzfkv fkipe s }tevktfke`v ie`i`v Fkehpe}kv ie`iè}` em`zèmè}`v2 dv`v 46? Vv}`v m` fkktmèmv 4=7 I mèvöe m` pe `vzfk w`f}kti 407 Teok 474 Fdk m` dv` 4?> Nziffke`v  `fpfke`v è m`tèfv 4?? Nziffke`v  fmèv m` Atbkw 4<<

447

4>0































































































































Fke}ècmk

FNZÁ]PIK

7

Kt}kokenicmnm s aáecakv fpnmtnmkv @H@AZIK CE]TKMPF]KTCK8

Ekt}`na`tcfnek

7 74 76 7= 70 77 7? 7<

FNZÁ]PIK

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6?6

T`nhpv}` mì Ecwì m` T`g`tèfcn

6?6

Ztkmpf}k e}`tkt) ikeo}pm s kt}kokeimm 6?0 Fkehpe}kv kt}kokei`v 6<= Ztks`ffke`v kt}kokei`v 63= @i ztkf`vk Ot!Vflm} =:4 Ztkdi`v m` áekv fpmtmkv =:3 Nziffke`v  kmìkv ie`i`v =>3 @vzfkv fke ztkmpf}k e}`tkt =4? Nziffke`v m` ikv `vzfkv fke ztkmpf}k e}`tkt @h`tffkv vpzi`è}tkv ===

=67

An}tcf`v vcaã}tcfnv s gktanv gktanv fpnmtî}cfnv fpnmtî}cfnv ==? @H@AZIK CE]TKMPF]KTCK8

api}cfneni ? ?4

Ztkf`vnacè}k m` caîoè`v

==?

Mokeixföe m` }tf`v vã}tfv Gktv fpmtî}fv =00

==3

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Zt`gnfck

I t`vzp`v} m` `v}pme}`v s ztk`vkt`v  iv zt`tv }t`v `mfke`v m` Îio`dtn ice`ni s vpv nzicfnfcke`v l vmk ps ot}gfe}` @v} }`tf`tn `mcfcöe nf}pnicxnmn ztkzktfke pe zksk vpv}efi }e}k zt i èv`þex fkk zt ì pvk m` }`fekikoá è ì fptvk Fkk e}`v) ì }`}k zt`vè} pe e}tkmpfföe ì`è}i km`te i îio`dt ie`i s pe zi vì`fföe m` e}`t`ve}`v ziffke`v @i }`ti `v ff`vdi`  `v}pme}`v ~p` lse m~ptmk i mpt`x e`f`vt) zkt ik oè`ti) è fîifpik) m`vzpãv m` fk! zi`}t v}vf}ktè}` mkv v``v}t`v m` }`î}fv  ewì pew`tv}tk I `} ztefzi mì }`}k `v spmt  ikv `v}pme}`v  mket ikv fkef`z}kv s iv ldimm`v dîvfv ~p` m`vzpãv p}ixtîe è vpv ftt`tv Ikv }`v efipmkv vopè iv t`fkèmfke`v mì Ie`t Nio`dt Fpttfpip V}pms Otkpz) Otkpz) iv fpi`v v` dve è pe ew`v}oföe fpmmkv fpmmkv m` iv e`f`vmm`v t`i`v m` ikv `v}pme}`v ` v}pme}`v s è pe fkevè!































































































































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Zt`gnfck

]tnevktanfcke`v ice`ni`v

Iv }tevktfke`v ie`i`v kte pe ’lik‑ ~p` v` è}t`}`h` è i }ì m` `v}` }`}k Vp p}ixföe `hkt ì vè}mk o`kã}tfk m` ik `vft}k Zkt `h`zik) è ì fzá}pik ) iv }tevktfke`v ie`i`v ztkzktfkee pe wvöe meîf s otîgf m` i pi}zi! fföe }tx!w`f}kt }tx!w`f}kt

Wnikt`v ztkzckv s vcv}ànv mceîacfkv

Ikv wikt`v ztkzkv zt`fè `~p}}wè}` ztke}k è ì }`}k) è ikv fzá}pikv 0 s ? Fkk `v}` }`ti v` `v}pm mpte}` wtv v`ev) ikv ipekv }èè îv }`zk mì pvpi zt dvktd`t s t`wvt `v}kv fkef`z}kv ftá}fkv Ikv wikt`v ztkzkv v` zife  vv}`v meîfkv mvft`}kv s fke}epkv) ikv fpi`v zt`fè è iv v`ffke`v :) =<) =3) s è fefk v`ffke`v mì fzá}pik 0 Niopekv fptvkv iiòe i fzá}pik 0 è pev fefk v`ev zp`v fpdtè iv v`ffke`v 4< s 43 è ipot mì fzá}pik = @v}v mkv v`ffke`v kzfkei`v zt`vè}e }kmkv ikv fkef`z}kv mì `vzfk w`f}kti efipmkv è ì fzá}pik =) vkv ~p` vke e`f`vtkv zt dktmt ì fzá}pik 0

Kt}kokenicmnm s ztkdiànv m` aáecakv fpnmtnmkv

@v}kv }`v t`fdè pe }t}è}k îv fkztèvdi` è fkztföe fke ì ~p` v` è! fpè}t fkøeè}` è ikv }`}kv dîvfkv @i Ie`t Nio`dt Fpttfpip V}pms Otkpz l è}xmk i e`f`vmm m` fke}t fke pe pemm vpv}efi è ikv ztkdi`v m` kt}kokeimm s áekv fpmtmkv) m`dmk  ~p` i kt}kokeimm fpzi` pe zzì zkt}e}` è ikv fîifpikv fkzp}fkei`v s è ì îio`dt ie`i epãtf) s zkt~p` ikv vv}`v ie`i`v efkevv}è}`v vptoè ps t`fpè}`è}` è ì }tdhk ztîf}fk

































































































































Zt`gnfck

w

]`ktànv s màkv}tnfcke`v

Ikv t`vpi}mkv zkt}e}`v v` `v}di`fè fkk }`kt`v K}tkv fkef`z}kv ø}i`v v` m`v! ziòe mè}tk m` t`fpmtkv ipemkv zt p}ixtv` fkk t``tèfv tîzmv I skt zt}` m` ikv }`kt`v }èè fkztkdfke`v kti`v) `vft}v zèvemk è ikv ipekv ztefze}`v @e iopekv fvkv) ikv fîifpikv `vèfi`v m` pe fkztkdföe v` p`v}te è pe `h`zik vì`ffkemk fpmmkvè}` Niopev Niopev w`tgffke`v m` tp}e v` m`he zt i v`fföe m` `h`tffkv) fpemk `v}k t`vpi} dèãgfk zt ikv `v}pme}`v

Ztkdiànv m` ztîf}cfn Ne}`v m` fm v`t` m` `h`tffkv zt`fè  zt`fè iopekv ztkdi`v m` ztîf}f vì`ffkemkv è kt fpmmkv I v`t` m` `h`tffkv w vòpm zkt vkipfke`v fkzi`}v @v}kv ztkdi`v v` èkfe è mgfpi}m`v zk}èfi`v ~p` zp`mè èfke}ttv` è i v`t` m` `h`tffkv k ztkzktfkee pe ’fiè}è}k‑ zt i `h`fpföe zkv}`tkt m` ikv `h`tf! fkv2 fke t`fpèf) iv vkipfke`v fke}èè vpo`tèfv k mw`t}èfv ø}i`v f`tf































































































































w

Zt`gnfck

]ànv fkazp}nfckeni`v

@i }`}k fpv ì zf}k m` i fkzp}mkt }e}k è ì m`vttkiik fkk è i ztîf}f mì îio`dt ie`i è iv fèfv s i eoè`tá Iv t`fpè}`v ek}v ep`tmv mtoè i }èföe lf vz`f}kv m` fözp}k s mv}eopè è}t` fkef`z}kv }`ötfkv) mokv i ew`tvöe ew`tvöe m` }tf`v) ` zi`è}fke`v m` fkzp}mkt) }i`v fkk iv f}ktxfk! e`v IP

FM NE@\K S VKZKT]@ @E IN T@M I `mföe f}pixm mì }`}k efips` pe fkz fkzi`} ,è eoiãv# m` i Opán m` `v}pmck ,V}pms Opcm`# è ì FM e`k @v} opán p` `vft} zt v`t pe zt}` e}òti mì fptvk Pe áfkek è ì }`}k mto`  ikv `v}pme}`v  vpdv`ffke`v `vz`fi`v m` i opán ~p` vpo`tè fök mket ikv fkef`z}kv fiw` mì fptvk I opán ztkzktfke pe vkipföe m`}iim  fm }`tf`t `h`tffk fke eø`tk zt) ik ~p` z`t}`  ikv VO































































































































Zt`gnfck

w

mì }`}k f}pixmk s ì zt`t fzá}pik m` i Opán m` `v}pmck ,è eoiãv# @v}` }`ti `v ztkzktfkemk zt spmt  ikv ztk`vkt`v  eft fke vp fptvk) }i fkk v pe idt`tá mv}tdps`t ì }`}k hpv}k e}`v m` ~p` iv fiv`v fkèxte Zt ikv `v}pme! }`v) ì v}k è t`m fke}è` lkhnv m` t`znvk s `|îaè`v m` ztîf}cfn ,fke vkipfke`v# ~p` fpdtè ikv }`v ztefzi`v mì }`}k Ztkwèè m` e`t mt`f} m` fptvkv ~p` ì p}kt l zt}mk è ikv øi}kv þkv Fm lkh m` t`zvk mè}gf m`gefke`v f iw`) }`kt`v s ldimm`v m` pe zt}` `vz`fágf mì }`}k

Nzicfnfcke`v zkt fnzá}pikv

@i v}k è i t`m }dãe fke}è` v`}` fvkv m` `v}pmk) ikv fpi`v ziáe ikv }`v e}tkmpfmkv i efk m` fm fzá}pik i otòt m}kv mì pemk t`i s kzkt}pemm`v zt ``f}pt pe `ziktföe îv ztkpem Zkt k}tk imk) îv m` w`e}` ztks`f}kv m` zifföe lfè `}èvwkv ikv }`v mì }`}k k e}tkmpfè ep`wv ziffke`v) fkk teptv fødfv) tp}v m` wpìk è `tkiáe`v) }tf`v m` mkeef è fkz`}èfv































































































































w

Zt`gnfck

L vmk pe ztwiòk }tdht fke Mwm Ftivke) Flti`v Hklevke) s Mpe` Zkt}`t è ì Ice`nt Nio`dtn Fpttcfpipa V}pms Otkpz Vpv m`v vkdt` i èv`þex mì îio`dt ie`i le epmk è `v}` }`}k m` pflv e`tv zkt}e}`v Notm`xfk m` e`t vef`t  ikv vopè}`v t`wvkt`v zkt vp eîivv fpmmkvk s vpv vpo`tèfv fkev}tpf}wv8 fkev}tpf}wv8

T`wcvkt`v m` in }`tf`tn `mcfcöe s `h`fp}kt`v m` ztp`dnv è finv` Mwm Npv}e) Otnem Wnii`s V}n}` Pecw`tvc}s O Dtdevke) Pecw`tvc}s k ]`|nv n} Npv}ce Bèe`}l Dtke) Fkteìi Pecw`tvc}s Mwm Ftivke) Vne Mcòk V}n}` Pecw`tvc}s Otò Fkee`t) Dtcolna Skpeo Pecw`tvc}s Fv`s ] Ft`ev) Pecw`tvc}s k Antsinem Vsiw` M`vHtmev) Kbnenone Pecw`tvc}s Fkiiò`

@ti Bsi) Fnicktecn V}n}` Pecw`tvc}s) Vnftnaè}k B}ltse Ièx) Pecw`tvc}s k Acee`vk}n!Mpip}l H~p`v I`e) Vstnfpv` Pecw`tvc}s @e!Deo Ie) Pecw`tvc}s k ]ki`mk Nemt` Ai}v`w) Pecw`tvc}s k Antsinem Ndtl Ae}ìi) Envvnp Fkaapec}s Fkiiò` Amlp Esbbebpzz) Pecw`tvc}s k































































































































Ek}n zntn ikv `v}pmcne}`v @v}` fptvk zp`m` v`t ì îv e}`t`ve}` s wikvk è}t` }kmv iv fiv`v m` }`î}fv



































































































































Ek}n zntn ikv `v}pmcne}`v

Ek}nv epaãtcfnv

V` t`fkèm i``t iv ek}v epãtfv efipmv è ì }`}k) efipvk v ek v` `v}î p}i! xemk pe fkzp}mkt k fifpimkt otîgf hpe}k fke ì idtk @e i wm t`i) i skt zt}` m` iv ziffke`v m` îio`dt ie`i zife fîifpikv ~p` `v}îe vph`}kv  ioøe `ttkt epãtfk) øe fpemk mflk `ttkt zp`m v`t ps z`~p`þk Iv ek}v epãtfv i`































































































































Ftv m` e`öe) 446 Ce}`tzkiföe m` zkiekkv) 4?) <= Cvkktgvk) ??) 40 A}tx hfkde) 4:3 Zkiekk m` Iop`tt`) 47 ]tevktmv ]tevktmv m` Izif`) =:) 4:4 Zkiekk m` Iòèmt`) =67 ]tevktfke`v ]tevktfke`v ie`i`v è fîifpik) 464!466) 643!66: _@D

_@D

_@D

Fcèfcnv ávcfnv Wo è wkimxk) 4<7 Fè}tk m` otw`mm) 63 T`ffke`v ~páfv) 03!7:) 76 Aii m` ftv}i) 4=<) 400 M`vfkzkvföe m` pe p`tx) 6<3 Vkemk otdmk mo}iè}`) 4?< @ieföe Opvve) =





























































































































































































































































> @fpnfcke`v ice`ni`v































































































































4

Fnzá}pik >

@fpnfcke`v ice`ni`v è îio`dtn ice`ni

Zkt ik }e}k) i fèf m` iv fkzp}mktv `v}î vöimè}` iom i îio`dt ie`i `me}` ì ft`fè}k `zikvwk m` ikv ztkf`vè}kv ztiìkv m` m}kv s ikv fîifpikv  ote `vfi

`me}` `zikvke`v fke zv}kiv m` t` Iv kemv t`dk}e è iv tkfv ~p` ls dhk i vpz`tgf` te s v` mè `zi`emk ` zi`emk o`ökekv fke`f}mkv  `}èvkv fdi`v ev}imkv m`dhk mì dtfk



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Algebra_Lineal_y_sus_Aplicaciones.jb.decrypted.pdf

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