Álgebra Lineal- Aplicaciones con Voyage 200

7/31/2019 lgebra Lineal- Aplicaciones con Voyage 200

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Djk`csdJfi`dj

^Dpjfhdhfbi`x hbi U`}dxFixusgìux \bvdk` 3??W

3?4?@i `xu` gdipdj ìhbiusdsx djfhdhfbi`x dsd ef|`sxbx u`gdx e`jk`csd Jfi`dj* xbjphfbidebs`x dxb d dxb dsd gdusfq fi|`sxd vKdpxx'Absedi* dx hbgb djfhdhfbi`x dsd ig`sbx fgdkfidsfbx*|`hubs`x v gx)

Gdu`sfd pdsd1Ubedx jdxFikìf`sdx

@@JJDDCCBBSSDDEEBB __BBSS11

FF))FF))IIKK@@JJKKDDSSHHDDLLFFKKPP@@SSBBDDMM@@SSIIIIEE@@QQ


2/65


3/65

^ DJK@CSD JFI@DJ W Fi|f`sib 3??6

Udcjd e` lpihfbi`x gdu`gufhdx bhb pxdedx dsd jd UF'\3?? _kfid 8

Udcjd e` lpihfbi`x gdu`gufhdx bhb pxdedx dsd jd UF'\3??

Lpihfi

Lbsgd e`

`xhsfupsd ìMBG@

E`xhsfhfi xfgj` @a`gjb)

\djbsdcxbjpub

dcx-`}s&

Xjb e`c`x u`hj`ds `xud hbgcfidhfie` jùsdx x`kpfeb e` jbx s`x`huf|bxdsiu`xfx e` d`supsd v hf`ss` hbi jd`}s`xfi eìusb)

Jbkdsfugbjbk-`}s& jbk-`}s*cdx`&

Xjb e`c`x u`hj`ds `xud hbgcfidhfie` jùsdx x`kpfeb e` jbx s`x`huf|bxdsiu`xfx e` d`supsd v hf`ss` hbi jd`}s`xfi eìusb* x`kpfeb e` pidhbgd v jd cdx` e`j jbkdsfugb* xf x`bgfu` x` ubgd hbgb cdx` 4?)

Sdq e`hpdjtpf`s

bseì

-`}s&Y-i"g&

E`c`x u`hj`ds sfg`sb jd `}s`xfitp` |d d `j`|dsx` d jd sdq eded* jp`kb`j xgcbjb e` buìhfd v ìus`dsiu`xfx jd ef|fxfihbss`xbiefìu` e` jd sdq tpùìkdx)

Hbx`hdiu` hxh-`}s&Xjb e`c`x u`hj`ds `xud hbgcfidhfie` jùsdx x`kpfeb e` jbx s`x`huf|bxdsiu`xfx e` d`supsd v hf`ss` hbi jd`}s`xfi eìusb)

X`hdiu` x`h-`}s&

Hbudikìu` hbu-`}s&

dsh hbxìb hbx'4-`}s&

_dsd jdx sfg`sdx us`x lpihfbi`xxfgj`gìu` u`hj`d 3ie . u`hjdxìb hbxìb udikìu`hbss`xbiefìu`) _dsd jdx jufgdx 8e`c`x ìusds dj gì e` lpihfbi`xusfkbibgusfhd hbi 3ie . ig`sb 0e` jd dsu` ipgsfhd v ìusds djxpcgì Usfk) v eds @IU@S xbcs` jdbhfi e`x`ded)

dsh xìb xì'4-`}s&

dshudikìu`

udi'4-`}s&

dshhbx`hdiu`

hxh'4-`}s&

dsh x`hdiu` x`h'4-`}s&

dshhbudikìu`

hbu'4-`}s&


4/65


iefh` Kì`sdj _kfid 5

iefh` Kì`sdj

F) Fiusbephhfi)0

FF) Eùdjj` Uhifhb));

FFF) Eùdjj` Kì`sdj e` U`hjdx))6

F\) Fiusbephfìeb edubx v `}s`xfbi`x hbss`hudgìu`44

\) iefh` e` jk`csd Jfi`dj)34

\F) Hbiuìfeb35'


5/65


Fiusbehhfi _kfid 0

Fiusbephhfi

Cfì|ìfeb dj hpsxb U`}dx Fixuspgìux \bvdk`3??* xu` hpsxb ufì` jd lfidjfede e` tp` dsìedx`j gdiàb `lfhfìu` v shufhb e` `xud hdjhpjdebsd ksdlfhdebsd gpv be`sbxd* vd tp` bx`` pi ksdi

hdgb e` djfhdhfi ì ubedx jdx fikìf`sdx v bs ìe` ì jd gdvbsd e` jdx gdu`sfdx tp` |`sx d

jb jdskb e` up hdss`sd* dsd tp` `xupef`x hbgb fikìf`sb v usdcda`x hbgb udj)

@xud hdjhpjdebsd xf cfì ufì` gphmd lpihfbidjfede v ksdi |ìudad* `x fgbsudiu` eàds ì hjdsb

tp` ib e`c` x`s pxded hbgb pi gèfb e` mdh`s usdgd b hbgb pi xpxufupub e`j dsìefqda`

fgdsufeb bs `j gd`xusb* xfib e` pi dbvb hjdsb v `x`hlfhb ì hded gdu`sfd dsd dkfjfqds

hjhpjbx v dsd ìuìe`s gàbs jbx u`gdx |fxubx ì hjdx`) Jdx gdu`sfdx ì jdx tp` u` pè` dvpeds

ksdie`gìu` e` usbihb hbgi -4* 3 v 8 x`g`xus`& xbi jdx xfkpfìu`x1

4) Tpgfhd Kì`sdj

3) Djk`csd Jfi`dj8) Hdjhpjb Efl`sìhfdj5) Hdjhpjb Fiu`ksdj0) @hpdhfbi`x Efl`sìhfdj`x


6/65


7/65


8/65


E`udjj` Uhifhb _kfid =

8) Hbjhdjd bs dusx dsd sbu`k`sjd g`abs)


9/65


Eùdjj` Kì`sdj e` U`hjdx _kfid 6

Eùdjj` Kì`sdj e` U`hjdx

Jd u`hjd EFDGDIU@ -pid u`hjd |`se` dj jdeb e` jd u`hjd BI&* dj s`xfbidsjd pid |`q dhuf|d ubedx jdxu`hjdx tp` uìkdi j`vìed |`se` xbcs` jdx u`hjdx ibsgdj`x) Xp lpihfi `x gjufj` v kì`sdjgìu`

u` `sgfu` e`xjdqdsu` ìus` sbksdgdx v hbilfkpsds hf`sudx djfhdhfbi`x e` jd dsu` kslfhd)

Jd u`hjd 3ie -u`hjd dqpj dj jdeb e` jd u`hjd EFDGDIU@&* dj s`xfbidsjd pid |`q dhuf|d ubedx jdx u`hjdx

tp` uìkdi j`vìed dqpj) Xp lpihfi sfihfdj `x hbgj`gìuds jdx `}s`xfbi`x ipgsfhdx* v ì

djkpibx hdxbx ìusds d gìx d|diqdebx)

Jdx u`hjdx L4'L=* x` pèì pufjfqds hpdieb ì jd diudjjd dds`qhdi bhfbi`x |dsfdedx ì jd dsu`

xp`sfbs* kì`sdjgìu` x` pxdi xjb dsd dcsfs gìx ì jbx sbksdgdx)

Jdx u`hjdx e`j Hpsxbs xfs|ì dsd gb|`su` ì kslfhdx* xbcs` jd ji`d e` ìusded v ì `j mfxubsfdj e`Mbg`* dx hbgb ì busbx sbksdgdx* u` fsx ldgfjfdsfqdieb hbi `j bhb d bhb)

Jd u`hjd D__X* e`xjf`kd `j gì kì`sdj e` jd hdjhpjdebsd* ebie` x` ìhpìusdi ubedx jdx

djfhdhfbi`x v sbksdgdx e` jd gfxgd)

Jd u`hjd GBE@* e`xjf`kd jd diudjjd dsd gbeflfhds jd hbilfkpsdhfi kì`sdj e` jd hdjhpjdebsd)

Jd u`hjd Xmflu* ufì` jd gfxgd lpihfbidjfede tp` jd u`hjd xmflu e`j u`hjdeb e` pid hbgpudebsd* dj

eàdsjb s`xfbideb v e`xjdqdsu` hbi `j hpsxbs e` pi jdeb d busb pè`x x`j`hhfbids pid x`sf` e`

Hpsxbs

_dsu` Ipgsfhd

U`hjdeb @}uìefebU`hjdx x`hfdj`x Xmflu*

EFDGDIU@* 3ie

U`hjdx L4'L=

U`hjd D__X

U`hjd HJ@DS

U`hjd @XH


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Eùdjj` Kì`sdj e` U`hjdx _kfid 4?

edubx b `}s`xfbi`x dsd e`xpx hbfdsjbx hbi jd hbgcfidhfi EFDGDIU@ . jùsd H* v `kdsjbx ì

hpdjtpf`s busd djfhdhfi hbi jd hbgcfidhfi EFDGDIU@ . jùsd \)

Jd u`hjd HJ@DS xfs|` e` lbsgd kì`sdj dsd cbssds jd ji`d e` ìusded e` jd hdjhpjdebsd v ìdjkpidx busdx djfhdhfbi`x cbssd kslfhdx v `j`gìubx gdshdebx dsd ksdlfhds)

Jd u`hjd @XH x` pxd dsd hdih`jds bhfbi`x m`hmdx b `ssbs`x hbgùfebx eìusb e` pi sbksdgd)


11/65


Fiusbehfìeb edubx , `}ps`xfbi`x hbss`hudgìu` _kfid 44

Fiusbephfìeb edubx v

`}s`xfbi`xhbss`hudgìu`

X` md eèfhdeb pi hdupjb hbgjùb d jd

`}jfhdhfi e` hgb fiusbephfs edubx v

`}s`xfbi`x hbss`hudgìu` e`cfeb d tp` x`

mdi feìuflfhdeb ipg`sbxbx `ssbs`x e`

`xhsfupsd ì gphmbx `xupefdiu`x d jd mbsd e`

u`hj`ds jbx edubx* jb hpdj `x e` |fudj

fgbsudihfd vd tp` e` u`hj`dsfihbss`hudgìu` jd filbsgdhfi ibx pè`

dssbads s`xpjudebx fihbss`hubx b gpv

efl`sìu`x d jb tp` tp`s`gbx ì s`djfede*

fie`ìefìu`gìu` e`j sbksdgd ì `j tp`

`xu`gbx xudx s`kjdx xbi dsd hpdjtpf`s

djfhdhfi ì `j tp` x` `xu usdcdadieb* `x

hbi|ìfìu` ubgdsx` pi uf`gb dsd

ìuìe`s v sdhufhds `xubx xìhfjjbx à`shfhfbx

dsd tp` `xhsfcdx hbss`hudgìu` jd

filbsgdhfi ì hded uds`d tp` s`xp`j|dx)

Xfkib Gìbx

@x fgbsudiu` tp` d jd mbsd e` u`hj`ds pid

`}s`xfi ì jd hdjhpjdebsd x` u`hj`` `j xfkib

gìbx de`hpdeb ì hded hdxb) X` e`c`

x`kpfs jd xfkpfìu` s`kjd1

Hpdieb x` `xhsfcd pid `}s`xfi ì jd tp`

x` fifhf` hbi xfkib i`kduf|b e`c` pxdsx` jd

u`hjd hbi xfkib i`kduf|b ìus` dsiu`xfx

) @xub gfxgb x` pxd hbi jdx

hdjhpjdebsdx hfìulfhdx mdcfupdj`x) \`s`gbx

pi ds e` à`gjbx) @ihfìe` up hdjhpjdebsd*

u`hjd BI1

Gp|ù` hbi `j hpsxbs d usd|x e` jdx

djfhdhfbi`x v bxfhfidu` ì MBG@ v ed

@IU@S1

_bs à`gjb* xf tp`s`gbx `xhsfcfs1

; =

Edgbx @IU@S 1

\`gbx tp` x` e`xjf`kd hbss`hudgìu` v x`

s`dhbgbed ì jd ji`d e` ìusded) @xu` `ssbs

e`j pxb e`j xfkib gìbx `x gpv hbgi v

e`c` pxdsx` vd x`d ì `j fifhfb e` pid

`}s`xfi b ì jd e` pi `}biìu` tp`

tp`sdgbx d pid buìhfd i`kduf|d b e`xpx

e` tp` x` md h`ssdeb pi dsiu`xfx) _dsd

cbssds jd ji`d e` ìusded u`hj`d HJ@DS)


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Xf x` mpcf`sd p`xub `j busb xfkib gìbx

mpcf`sd xdjfeb pi s`xpjudeb hbgjùdgìu`

efl`sìu` ` fihbss`hub) Busb à`gjb1

\`gbx tp` x` j`` hbss`hudgìu`* xf

mpcfsdgbx p`xub `j xfkib hbiusdsfb1

\`gbx tp` ibx fiefhd tp` mdv pi `ssbs e`

xfiud}fx ì jd ji`d e` ìusded)

@i hpdjtpf`s busd bxfhfi e` pid

`}s`xfi tp` ib x`d `j fifhfb* `j xfkib

i`kduf|b tp` e`c` pxdsx` `x `j e` jd u`hjd

cjdihd )

_bs à`gjb1

= 4 8_dsd `j sfg`s usgfib hbgb `xud dj fifhfb x`

pxd `j xfkib gìbx e` jd u`hjd i`ksd v dsd `jjufgb usgfib x` pxd `j xfkib gìbx e` jd

u`hjd cjdihd1

Hbgb uf be`gbx e`hfs tp` ì jd ji`d e`

ìusded `j xfkib gìbx e` jd u`hjd i`ksd `xu

pi bhb gx `tp`b v gx dssfcd tp` `j e`

jd u`hjd cjdihd)

_dsiu`xfx

@j pxb hbss`hub e` jbx dsiu`xfx `x gpv

fgbsudiu` vd tp` e` fkpdj gdi`sd |d d

e`lfifs ip`xusdx `}s`xfbi`x) Jbx dsiu`xfx

ef|feì `}s`xfbi`x hbgjùdx ì jd ji`d e`

ìusded e` jd hdjhpjdebsd* mdv djkpidx

lpihfbi`x hbgb jd lpihfi `}biìhfdj*

jbkdsfugb idupsdj b jdx usfkbibgusfhdx tp`

hpdieb jb u`hj`dx figèfdudgìu` u` dcs` pi

dsiu`xfx v jb mdh` hbi jd lfidjfede e` tp`

e`lfidx hbss`hudgìu` jb tp` |d eìusb e`

`xd lpihfi) @x fgbsudiu` s`hbseds tp`

Ubeb dsiu`xfx tp` x` dcs` e`c`

h`ssdsx`) _bs à`gjb xpbikdgbx tp`

e`x`dgbx xhsfcfs1

xfi;= j i Dj u`hj`ds jd lpihfi e` xìb x` dcs`

dpubgufhdgìu` `j dsiu`xfx `

figèfdudgìu` e`xpx e`c`gbx `xhsfcfs


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14/65



\`gbx tp` dj eds @IU@S jd hdjhpjdebsd

ìufìe` busd hbxd hbgjùdgìu` efxufiud)

@x pi gpv cpì uf tp` bcx`s|`x jb tp`

`xhsfcfxu` dj eds @IU@S ì jd dsu` fqtpf`sed

e` jd diudjjd v |`dx xf `xd `}s`xfi `x jd

tp` tpf`s`x)

Busb à`gjb1

=; 8 4 0

Hbgb ì `j ipg`sdebs v eìbgfidebs mdv

gx e` pi usgfib e`cì `xhsfcfsx` dgcbx

dsiu`xfx dj fifhfb v dj lfidj e` hded

`}s`xfi* edgbx @IU@S1

Iu`x` tp` ì `j eìbgfidebs hbgb jd`}s`xfi fifhfd hbi pi usgfib hbi xfkib

i`kduf|b x` `gf`qd pxdieb `j gìbx e` jd

u`hjd i`ksd* v `j xfkpfìu` `x hbi jd u`hjd

gìbx cjdihd) S`hbse`gbx tp` jbx

dsiu`xfx ef|feì `}s`xfbi`x hbgjùdx*

bs `xb dpitp` `xu` ì gèfb e` jd ji`d e`

ìusded x` pxd `j xfkib i`kduf|b i`ksb)

Udgcfi ibudgbx tp` jd hdjhpjdebsd

ldhubsfqd jd dsu` e` dssfcd v hdgcfd xfkibx

bs hbgbefede* xfìeb `xub pid fkpdjede

`}dhud)

@}biìu`x

Busb `ssbs s`jduf|dgìu` hbgi xbi jbx

`}biìu`x) _bs à`gjb xf tp`s`gbx

`xhsfcfs1

Hbgb |`sdx d xfgj` |fxud ì jd hdjhpjdebsd

ib `}fxu` pid u`hjd hbi sdq hcfhd* xbjb `xud

jd e` sdq hpdesded* dsd `xhsfcfs pid sdq e`j

bseì tp` x`d x` e`c` pxds `j `}biìu` hbi

jd xìhfjjd s`kjd1

Hpdieb x` `xhsfc` pi `}biìu` ì

lsdhhfbi`x ì jd hdjhpjdebsd* e` fkpdj

gdi`sd e`c` bi`sx` ìus` dsiu`xfx

e`xpx e`j xgcbjb e` `}biìu 1

Dj eds @IU@S |`gbx jd `}s`xfi hbss`hud e`

jd `tpfx hbi xp `}biìu`) E` fkpdj gdi`sd

x` s`hdjhd jd fgbsudihfd e` bi`s ìus`

dsiu`xfx `xud `}s`xfi vd tp` e` ib

mdh`sjb jd hdjhpjdebsd ìuìe`s busd hbxd*

bcx`s|d1


15/65



\`gbx tp` dj ib bi`sjb jd hdjhpjdebsd

ìufìe` tp` x` usdud e` pid `tpfx hpdesded

ìus` us`x v ib `x jd `}s`xfi de`hpded) _bs`xb `x GPV FG_BSUDIU@ `j `xhsfcfs

hbss`hudgìu` jd filbsgdhfi ì jd

hdjhpjdebsd vd tp` e` ib mdh`sjb ibx eds

s`xpjudebx fihbss`hubx)

Jfxudx Gdusfh`x

Hpdieb `xhsfcdx ì jfxudx b gdusfh`x

-kì`sdjgìu` jdx pxdsdx ì gdu`sfdx hbgb

Djk`csd Jfi`dj* Fi|`xufkdhfi e` B`sdhfbi`x4* Fikìf`sd @hbigfhd 4* Fikìf`sd

@hbigfhd 3& `x fgbsudiu` tp` s`hp`se`x

tp` jdx hbgdx * udgcfi ef|feì

`}s`xfbi`x v bs jb udiub xf bs à`gjb

`xhsfc`x pi edub hbi xfkib i`kduf|b `x hbgb

xf fifhfdsd pid ip`|d `}s`xfi v e`c`

u`hj`dsx` hbi `j xfkib gìbx e` jd u`hjd

i`ksd)

_bs à`gjb dj `xhsfcfs jd jfxud1

0*


16/65


Fiusbehfìeb edubx , `}ps`xfbi`x hbss`hudgìu` _kfid 4 bs jb udiub ì jd

hdjhpjdebsd be`gbx mdh`s jb xfkpfìu`1

4) Cbssdgbx jd ji`d e` ìusded v u`hj`dgbx1

dY'4!eù-d&1

3) Edgbx @IU@S1

V jfxub* bcuì`gbx jd gdusfq deapiud)

S`hp`sed tp` xf e`x`dx hbjbhds ig`sbx

fgdkfidsfbx ì up gdusfq xbjb `xhsfc` 3ie .

jùsd F e`j u`hjdeb `}uìefeb)


49/65


Gdusfq Usdixp`xud _kfid 56

Gdusfq Usdixp`xud

E` fkpdj gdi`sd -dpitp` `x gpv xìhfjjb d

gdib& u pè`x udgcfi mdh`s jd gdusfq

usdixp`xud ì jd U`}dx) Hbixfe`s`gbx jd

gfxgd gdusfq hbi jd tp` m`gbx `xudeb

usdcdadieb1

3 8 4 4 8 ?3 4 5D

V i`h`xfudx jd gdusfq usdixp`xud) _dsdmdh`sjd usdixp`xud xfgj`gìu` u`hj`dgbx

jd |dsfdcj` d ì jd ji`d e` ìusded hbgb vd

xdc`gbx v e`c`gbx jjdgds dj gì

gdu`gufhb 3ie . ig`sb 0 e` jd dsu`

ipgsfhd1

Dmbsd e`xj`kdgbx `j gì e` Gdusf} vx`j`hhfbidgbx jd sfg`sd bhfi tp` `x pid`tp`d jùsd U `j`|ded ì `}biìu` vedgbx @IU@S1

Dmbsd xfgj`gìu` edgbx @IU@S v |`gbx jdgdusfq usdixp`xud1


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@hpdhfbi`x Gdusfhfdj`x _kfid 0?

@hpdhfbi`x Gdusfhfdj`x

E` fkpdj lbsgd jd U`}dx u` pè` dvpeds d

s`xbj|`s `hpdhfbi`x hbi gdusfh`x tp` uèàì s`xbj|`s v hbgsbcds upx `hpdhfbi`xv"b s`xp`xudx) Xpbikdgbx tp` u` eàdis`xbj|`s jb xfkpfìu`1

Ededx jdx gdusfh`x1

4 44 3 4 ?? 3 ? 44 ?D C H

S`xbj|`s jd `hpdhfi1 _dsd s`xbj|`s `xud `hpdhfi ì jd U`}dx

e`c`gbx sfg`sb ibgcsds hded pid e` jdx

gdusfh`x D* C v H hbgb vd xdc`gbx1

Dmbsd udgcfi e`c`gbx hs`ds pid gdusfqtp` |d d x`s jd gdusfq s`xp`xud* pufjfqds`gbxjdx |dsfdcj`x {*}*v*q v jd ibgcsds`gbx hbi jd

|dsfdcj` s bs x`s jd gdusfq s`xp`xud1

S

Vd tp` m`gbx hs`deb ubedx jdx gdusfh`x*cbssdgbx jd ji`d e` ìusded hbi u`hjd HJ@DSv dmbsd xfgj`gìu` u`hj`dgbx udj hpdj jd`hpdhfi d ìhbiusds* bc|fdgìu` e`c`gbxmdh`s jd s`jdhfi e` tp` ] `x `tpf|djìu` d

ip`xusd S1

Edgbx @IU@S v |`gbx1

\`gbx tp` b`sd jdx gdusfh`x v hs`d pidgdusfq hbi hpdusb `hpdhfbi`x v 5 fihkifudxtp` xbi jdx fihkifudx d ìhbiusds) Cbssdgbxjd ji`d e` ìusded hbi u`hjd HJ@DS) Dmbsde`c`gbx dxds xud gdusfq d pid jfxud* dsd`xub e`xj`kdgbx `j gì gdu`gufhb hbi3ie. ig`sb 0 e` jd dsu` ipgsfhd1


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@hpdhfbi`x Gdusfhfdj`x _kfid 04

Jp`kb e`xj`kdgbx `j gì e` Jfxu vx`j`hhfbidgbx jd jufgd bhfi e` jd jfxudtp` `x jd bhfi L* tp` `x jd lpihfigdujfxu- v edgbx @IU@S dsd tp` x`hbf` d jd ji`d e` ìusded1

Dmbsd dsd fiusbephfs jd gdusfq tp` `x jd tp`dhdcdgbx e` ìhbiusds edgbx hbi `j hpsxbsmdhfd dssfcd pid |`q dsd xbgcs`ds jd gdusfqs`xpjudeb v edgbx @IU@S dsd tp` x` hbfèfs`hudgìu` d jd ji`d e` ìusded1

V dmbsd xbjb h`ssdgbx jd lpihfi hbi `jdsiu`xfx e` hf`ss` v edgbx @IU@S1

@xu` dxb lp` xbjb dsd bseìds jdx`hpdhfbi`x* cbssdgbx jd ji`d e` ìusded hbiu`hjd HJ@DS v dmbsd jjdgdgbx jd lpihfi

xbj|`- dsd s`xbj|`s `j xfxu`gd e``hpdhfbi`x* xdc`gbx tp` `xu ì `j gì e`Djk`csd s`xfbidieb L31

Dmbsd dsd fiefhdsj` tp` jdx `hpdhfbi`x xbijdx e` dssfcd e` fkpdj gdi`sd edgbx mdhfddssfcd hbi `j hpsxbs pid |`q v edgbx @IU@Sdsd tp` x` hbf` d jd ji`d e` ìusded1

V dmbsd dsd fiefhdsj` tp` tp`s`gbx tp`s`xp`j|d jdx 5 fihkifudx e` ubedx jdx

`hpdhfbi`x u`hj`dgbx sfg`sb pid hbgd **jp`kb dcsfgbx pid jjd|` hbi 3ie v `jdsiu`xfx e` d`supsd - v jp`kb jdx|dsfdcj`x tp` e`x`dgbx tp` ìhpìusèf|fefebx bs hbgdx -{*}*v*q&*figèfdudgìu` e`xpx h`ssdgbx jd jjd|`hbi 3ie . dsiu`xfx e` hf`ss` v bs jufgb`j dsiu`xfx ibsgdj tp` hf`ssd jd lpihfixbj|`1


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Edgbx @IU@S v e`xpx e` pibx fixudiu`x|`gbx1

V `xud `x jd xbjphfi e` hded edub ì jdgdusfq S) Cbssdgbx jd ji`d e` ìusded hbiu`hjd HJ@DS v dmbsd dsd |`s jd gdusfq hbgbe`c` x`s xbjb u`hj`dgbx ip`xusd gdusfqs`xpjudeb `x e`hfs jd |dsfdcj` s v dmbsdxdhdgbx `j b`sdebs {fum hbi 3ie .jùsd N e`j u`hjdeb `}uìefeb1

@j b`sdebs {fum bies jb tp` tp`sdgbxì jd gdusfq fiefhiebj` jbx |djbs`x e` jdx|dsfdcj`x* e` fkpdj lbsgd u`hj`dgbx pid |`qmdhfd dssfcd hbi `j hpsxbs dsd xbgcs`ds jbxs`xpjudebx e` jbx edubx v edgbx @IU@S dsdtp` x` hbfì ì jd ji`d e` ìusded1

_dsd lfidjfqds edgbx @IU@S v |`gbx jd gdusfqhbi jdx bxfhfbi`x e` jbx edubx ì s`xpjudeb1

V jfxub m`gbx jj`kdeb d jd gdusfq s`xpjudiu`*`x e`hfs jd gdusfq ] tp` ibx èdi) E` `xudlbsgd pè`x hbgsbcds upx s`xp`xudx)

\`dgbx busb à`gjb) U` feì ìhbiusdsJbx |djbs`x e` ]* V v Q tp` xdufxldhì jd`hpdhfi1

448 480

438 ???

E` fkpdj lbsgd `xub x` pè` fiusbephfsefs`hudgìu` ì jd ji`d e` ìusded pxdiebsfg`sb jd lpihfi xbj|`-1

Jp`kb fiusbephfgbx udj hpdj jd `hpdhfi ds`xbj|`s hbi jdx gdusfh`x v jdx |dsfdcj`x tp`cpxhdgbx* s`hp`sed tp` e`c`x cbssds jdx|dsfdcj`x tp` vd uìkdx dxfkidedx hbi pi|djbs ì jdx |dsfdcj`x }* v v q* `xub jb pè`x

mdh`s lhfjgìu` s`xfbidieb L< v edieb@IU@S 3 |`h`x1


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Dmbsd `xhsfcfgbx udj hpdj jd `hpdhfi hbgbmdcdgbx efhmb1

U`sgfidgbx e` `xhsfcfs jd `hpdhfi1

Fkpdj tp` ì `j à`gjb diu`sfbs hbgbèfgbx s`xp`xud e` gx e` pid |dsfdcjè`c`gbx bi`s ìus` jjd|`x ubedx jdx|dsfdcj`x tp` e`x`dgbx tp` ìhpìus`-}*v*q& v h`ssdgbx hbi `j dsiu`xfx e` hf`ss`dj lfidj* edgbx @IU@S v |`gbx1

V |`gbx `j s`xpjudeb) Hbi `xu` à`gjb u`pè`x eds hpìud e` 3 hbxdx* 4 `x tp` mdvpidx dssbcdx hbi pi ig`sb dj jdeb ì jbxs`xpjudebx* `xub xfkiflfhd tp` mdv pidhbixudiu`* `x e`hfs tp` `xu` xfxu`gd e``hpdhfbi`x ufì` pi ig`sb filfifub e`xbjphfbi`x) U jb pè`x hbgsbcdsxpxufupvìeb jd dssbcd5 -jd dssbcd hbi piig`sb dj jdeb xbjb fiefhd `j ig`sb e`

hbixudiu` tp` jj`|d ì `j bseì hsbibjkfhbe` jd hdjhpjdebsd* `sb ì s`djfede `x pidhbixudiu` hpdjtpf`sd* IB xfgcbjfqd jdb`sdhfi e` pi ig`sb 5& bs pi ig`sbhpdjtpf`sd v b`sdieb jdx busdx `}s`xfbi`x*xf u` lfadx ubeb fifhfd ì jd |dsfdcj` Q tp` ibxefh` tp` pè` x`s pi ig`sb hpdjtpf`sd*jp`kb jd |dsfdcj` ] e`c` x`s fkpdj d `x`gfxgb ig`sb hpdjtpf`sd ìus` 5 v dsd Ve`c` x`s `x` gfxgb ig`sb hpdjtpf`sdgpjufjfhdeb bs ) Udgcfi u` pè`x eds

hpìud e` tp` ì `j à`shfhfb diu`sfbsup|fgbx tp` hs`ds pid gdusfq s`xpjudeb dsd|`s jbx edubx e` `xud gdusfq* ì `xu` hdxb ib

up|fgbx tp` mdh`sjb e`cfeb d tp` jdx|dsfdcj`x ]* V v Q xbi pi ig`sb `xhdjdshpdjtpf`sd)


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\`hubs`x _kfid 05

jk`csd e` \`hubs`x

\`hubs`x

Dmbsd dsd s`xbj|`s |`hubs`x ì jd U`}dx x`

e`c` mdh`s djkb xfgfjds hbi jb tp` mfhfgbx

hbi jdx gdusfh`x* dmbsd x` mdsi jfxudx ì

jpkds e` gdusfh`x) @a`gjb) U` feì xpgds*

s`xuds* gpjufjfhds* ìhbiusds `j ikpjb

ìus` dgcbx* sbephub piub v sbephub

hspq e` `xubx 3 |`hubs`x1

** * * Jb sfg`sb tp` mdv tp` mdh`s hbgb vdxdc`gbx `x cbssds jd ji`d e` ìusded* dmbsd

cfì `xhsfcdgbx `j sfg`s |`hubs1

4) _s`xfbidgbx u`hjd 3ie .u`hjd

dsiu`xfx e` d`supsd * |`gbx tp` x`

dcs` pid jjd|`* dmbsd xfgj`gìu`

u`hj`dgbx jbx |djbs`x e`j sfg`s |`hubs

x`dsdebx bs pid hbgd1

3) Dmbsd h`ssdgbx jd jjd|` s`xfbidieb

3ie . u`hjd dsiu`xfx e` hf`ss` v

jd jjdgds`gbx p s`xfbidieb u`hjd .

jùsd P e`j u`hjdeb `}uìefeb1

8) Edgbx @IU@S v |`gbx1

Mdh`gbx jb gfxgb dsd `j x`kpieb |`hubs*

dcsfgbx jdx jjd|`x* v u`hj`dgbx jbx |djbs`x e`j

x`kpieb |`hubs* xjb tp` dmbsd jjdgds`gbx

d xu` x`kpieb |`hubs | 1

M`gbx dxfkideb jfu`sdj`x d ip`xusbx

|`hubs`x* dmbsd mds`gbx hded pid e` jdx

b`sdhfbi`x xbjfhfudedx)


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B`sdhfbi`x hbi \`hubs`x _kfid 00

Xpgd

Cbssdgbx jd ji`d e` ìusded hbi jd u`hjd

HJ@DS v dmbsd xfgj`gìu` u`hj`dgbx p.|1

Edgbx @IU@S v |`gbx `j |`hubs s`xpjudiu`1

S`xud

Dx hbgb |f`sbi e` xìhfjjb tp` `x jd xpgd*

vd mdcsi eèphfeb hbgb x` s`xud*

xfgj`gìu` u`hj`dgbx p'| vedgbx @IU@S1

Gpjufjfhdhfi

Fkpdjgìu` jb ifhb tp` x` i`h`xfud mdh`s `x

`xhsfcfs ì jd ji`d e` ìusded p!|

v edgbx @IU@S1


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57/65

^ DJK@CSD JFI@DJ W

ikpjb ìus` 3 |`hubs`x

ikpjb ìus` 3 \`hubs`x

_dsd s`xbj|`s `j ikpjb ìus`

e`c`gbx s`hpssfs d jd lsgpj

4) _sfg`sb e`c`gbx `xhs

fi|`sxd e`j hbxìb* dsd `

mdc`s cbssdeb jd ji`d e` ì

3ie . u`hjd 1

Dmbsd cfì* xdc`gbx tp` `j

lsgpjd `x `j sbephub piu

e` s`xbj|`s* bs jb udiub i

mdhfd dssfcd ì

xbgcs`dgbx `j ; tp` lp` `j s

Vd xbgcs`deb j` edgbx @IU

hbfd efs`hudgìu` d jd ji`d

Dmbsd u`hj`dgbx `j xfkib e`

dcsfgbx pi dsiu`xfx 1

dgcbx |`hubs`x

1

fcfs jd lpihfi

xub e`xpx e`

sded* u`hj`dgbx

pg`sdebs e` jd

b tp` dhdcdgbx

bx e`xjdqdgbx

`j mfxubsfdj v

`xpjudeb1

S v x`

e` ìusded1

f|fxfi v

Dmbsd dcsfgbx jd sdq s

u`hjd 1

IBUD FG_BSUDIU@1

@x gpv fgbsudiu`

dsiu`xfx tp` x` dcs`

`xub pè` s`xpjuds ì

tp`s`s |`s `j s`xpju

s`xpjudebx fihbss`hubx)

3) Xfkpfìeb hbi `j à`

`xhsfcfs pid lpihfi e

xpgds jbx `j`gìubx `

xpg-

8) @xhsfcfgbx jd jfu`sdj

|`hubs p `j`|deb d

v h`s

jp`kb j xfkib bs 1

5) Jjdgdgbx e` ip`|b

mdh`gbx jb gfxgb dsd

Fi|f`sib 3??6

_kfid 0;

`xfbidieb .

x`djds tp` ubeb

e`c` h`ssdsx` vd tp`

i `ssbs e` xfiud}fx dj

deb hbijj`|ds d

shfhfb dmbsd |dgbx d

xpgd jd hpdj |d d

i jd jfxud `xhsfcfgbx

1

e` ip`xusb sfg`s

jd x`kpied buìhfd

dgbx `j dsiu`xfx*

jd lpihfi xpg- v

`j x`kpieb |`hubs \1


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ikpjb `ius` 3 |`hubs`x _kfid 0=

0) Dmbsd dsd lfidjfqds be`gbx |`s tp` mdv

8 dsiu`xfx xfi h`ssds* bs jb udiub

u`hj`dgbx 8 |`h`x `j dsiu`xfx e` hf`ss`


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\`hubs`x hbi \`hubsx _kfid 06

\`hubs`x hbi \`hubsx

Udgcfi ì ubedx jdx hdjhpjdebsdx fixudj `j

sbksdgd |`hubsx-& `j hpdj e` fkpdj lbsgdìhpìusd gx lhfjgìu` jbx jufgbx

|djbs`x* sbephub piub* sbephub hspq v

ikpjb ìus` `jjbx hbi xbjb fiefhds xpx

hbbseìdedx* pèì `xuds ì 3 8

efgìxfbi`x)

@i jd ji`d e` ìusded e` MBG@ u`hj`d

|`hubsx-& v ed @IU@S1

V ibx `g`qds edieb d `xhbk`s jd

efgìxfi e` jbx |`hubs`x 3E 8E*

x`j`hhfbidgbx 8E v edgbx @IU@S1

Jp`kb ibx s`kpiud hpiubx |`hubs`x x` |di

d ìhbiusds xudx sbfède`x*

x`j`hhfbidgbx 3 \`hubsx v edgbx @IU@S1

V dmbsd xfgj`gìu` jjìdgbx jdx

hbbseìdedx e` hded |`hubs tp` ibx edi1

Edgbx @IU@S dsd hbiufipds v jjìdgbx jdx

hbbseìdedx e`j x`kpieb |`hubs1

Edgbx @IU@S 3 |`h`x v |`gbx1

Ibx ed bs sfihffb `j _sbephub piub tp`

`x `j gfxgb tp` vd mdcdgbx ìhbiusdeb ì

MBG@ v jp`kb jd gdkifupe e` hded |`hubs)

Edgbx @IU@S dsd hbiufipds v |`gbx1

Ibx gp`xusd `j ikpjb ìus` dgcbx* tp` `x

`j gfxgb |djbs tp` mdcdgbx ìhbiusdeb ì

MBG@ v bs jufgb ì hbjpgid `xu `j

sbephub hspq 3 f '8a '5n) _dsd u`sgfids `j

sbksdgd edgbx @XH L01

Hbi `xub hbihjpfgbx `j hpsxb e` jk`csd

Jfi`dj dbvdeb hbi jd hdjhpjdebsd UF\3??*

`x`sb tp` v` mdvd xfeb e` pufjfede v j` e`x

pi cpì pxb) S`hp`sed tp` hpdieb |dvdx d

usdcdads ì gdu`sfdx hbgb Hjhpjb Fiu`ksdj v

efl`sìhfdj e`c`x s`ks`xds jd hbilfkpsdhfi

e` up hdjhpjdebsd d Sdefdi`x) U` s`hbgfìeb


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\`hubs`x hbi \`hubsx _kfid


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@a`shfhfbx _sbp`xubx _kfid


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@a`shfhfbx _sbp`xubx _kfid


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Álgebra Lineal- Aplicaciones con Voyage 200