Solución de SEL de Orden 3 Por Determinante La Clase

 

  JF[I@ÙE LK KF LK JWLKE9 ^JW LK\KWO@EAE\K

Ijes`lkrkojs kf YKF lk jrlke 9 a1 x + g1 y + i 1 z ? l 1 a 7 x + g7 y + i 7 z ? l 7 a 9 x + g9 y + i 9 z ? l 9

, ljelk fjs a ` , g` , i ` , l ` ∃ W para ` ?1,7,9. Ketjeiks  x ?

| x| | y| | z| , y ? , z? |Y| |Y| |Y|

, ljelk

| | |

| | | | | l1   g1   i1

a1   l 1   i 1

a 1   g1   l 1

a1   g1   i 1

  g 7   i 7 ,| y|? a7   l 7   i 7 ,| z|? a 7   g7   l 7 ,|Y|? a7   g 7   i 7 a9   g 9   i 9 a 9   g9   l 9 a9   l9   i 9 l9   g9   i9

| x|? l

7

Kdkri`i`j. Wksjfvkr kf s`stkoa lk kiuai`ùe f`ekaf pjr lktkro`eaetk 1.   7 x + 9 y + ; z ?77  9 x + <  y + 7 z ? 12  ; x + 7 y + 9 z ?7 1 

1

 

7.   x + 7 y ∗9 z ?∗<   ∗ x + y + ; z ?1  7 x ∗ y ∗ z ?∗ 7 

9.   ∗7 x + 9  y ∗ z ?=  <  x ∗7  y + ; z ?∗9   x + 7 y ∗9 z ?> 

7

 

 (7) 9 x ∗ y ∗ + 19 + = ?1> Kf lktk lktkro ro`e `eae aetk tk | x|  sk jgt` jgt`kek kek rkopf rkopfaz azael aeljj ke fa ij ijfu fuoe oeaa lk  x   fa ijfuoea lk rksuftaljs, asï ∗1 1   ∗ 1 | x|? > 7 9 ?∗1 (∗3 + 9 )∗1 ( >∗9 )∗( > ∗7 )?∗(∗; )∗(∗9 ) ∗(∗7 ) 1   ∗1   ∗ <

|

|

| x|? 1>

Kf lktk lktkro ro`e `eaet aetkk | y|  sk jg jgt` t`ke kekk rk rkop opfa fazae zaelj lj ke fa ijfu ijfuoe oeaa lk  y   fa ijfuoea lk rksuftaljs, asï 7   ∗1   ∗1 | y|? 1 > 9 ?7 (∗9 ) +(∗< ∗ 0 )∗1?∗2∗19 ∗1?∗7> 9 1   ∗<

|

|

Kf lktk lktkro ro`e `eaet aetkk | z|  sk jgt` jgt`kek kek rkopf rkopfaz azael aeljj ke fa ijfu ijfuoe oeaa lk  z   fa ijfuoea lk rksuftaljs, asï 7 1   ∗1 | z|? 1 7 > ? 7 ( 7∗ > )∗( 1 ) ∗(∗1∗2 )?< ∗1 += ?1> 9   ∗1 1

|

 |

Wkopfazaelj

| x| 1> | y| | z| ? ?1 , y ? ? ∗7> ?∗7  y z ? ? 1> ?1 |Y| 1> |Y| 1> |Y| 1> Rkr`b`iaelj

 x ?

Ke (1)   7 x + y ∗ z ?∗1 7 ( 1 )+(∗ 7 )∗1?∗ 1 ∗7∗1 ?∗1     ∗1?∗1

Ke (7)    x + 7 y + 9 z ? > 1 + 7 (∗7 )+ 9 (1 )?> 1∗ < + 9 ?>     >º >

Ke (9)   9 x ∗ y ∗  x ∗ y ∗ z ?<

∗ x + 7 y ∗9 z ?∗9  7 x ∗ y ∗7 z ?∗<    x + y ∗; z ?1

∗7 y ∗ z ?1 7 x + 9  y ∗ z ?<    x ∗ y + 7 z ?=

7 x + y ∗ z ?∗ 1 9 x ’ 7 y + z ?9

 x + z ∗1  x + y ?>

 x + y + z ?∗7 7 x ’ y + z ?1

∗

 x ’ 7 y + 7 z ?9  x ’ 7 z ?<  y ’ z ?1

^rjgfkoa lk Apf`iai`ùe4

1. [ea ágr`ia ágr`ia prjl prjluik uik trk trkss t`p t`pjs js lk iao`sa iao`sas. s. Iala uej lk fjs trks t`pjs t`pjs lk iao`sa iao`sa t`kek quk pasar pjr trks lkpartaoketjs lk prjluii`ùe4 ijrtk, ijs`lj y kopaquk. Ykmôe kf t`pj lk iao`sa, kf t`kopj lk tragadj quk sk jiupa ke iala uea kstá lalj ke fa s`mu`ketk tagfa4 \`pj A >.7 cr >.9 cr >.1 cr

Lkpartaoketj lk ijrtk Lkpartaoketj lk ijs`lj Lkpartaoketj lk kopaquk

\`pj G >.< cr >.; cr >.7 cr

\`pj I >.9 cr >.< cr >.1 cr

Fjs lkpartaoketjs lk ijrtk, ijs`lj y kopaquk t`keke l`spje`gfks ijoj oáx`oj 112>, 1;2> y cjras lk tragadj pjr skoaea rkspkit`vaoketk. ºIuáetas iao`sas lk iala t`pj lkgk lk prjlui`rsk a fa skoaea para jiupar af oáx`oj fa iapai`lal lk iala lkpartaoketj: Ksir`g`ojs kf s`stkoa lk kiuai`jeks, ijes`lkrkojs  x fa iaet`lal lk iao`sas t`pj A,  y fa t`pj G y  z  fa t`pj I >.7 x + >.<  y + >.9 z ?112> ( 1 ) >.9 x + >.;  y + >. ( 7 ) >.1 x + >.7 y + >.1 z ? ( 9 )

Caffaojs fjs lktkro`eaetks >.7

| |

|Y|? >.9 >.1

>.<

>.9

>.; >.7

>.< >.1

|

?>.7 ( >.>; ∗>.>3 )∗>.< ( >.>9∗>.>< ) + >.9 (>.>2 ∗>.>; )

|Y|?∗>.>>2 + >.>>< + >.>>9 ?>.>>1

|

112>

>.<

>.9

| x|? 1;2>

>.;

>.<

>.7

>.1



?112> ( >.>;∗ >.>3 )∗>.< ( 1;2 ∗107 ) + >.9 (917 ∗7)

| x|?∗9

>.9

| y|? >.9

1;2>

>.<



>.1

>.1

? >.7 ( 1;2 ∗107 )∗112> ( >.>9 ∗>.>< )+ >.9 ( 1.7

>.<

112>

| z|? >.9

>.;

1;2>

>.1

>.7



|

|

?>.7 ( 7∗ 917 )∗>.< ( 1 (>.>2 ∗>.>; )

| z|?∗1 , y ? ?   >.3 ?3>> y z ? ?   7 ?7>>> |Y| >.>>1 |Y| >.>>1 |Y| >.>>1

Rkr`b`iaelj Ke (1) >.7 x + >.<  y + >.9 z ?112> >.7 ( 17>> )+ >.< ( 3>> )+ >.9 ( 7>>> )?112> >.7 ( 17>> ) + >.< ( 3>> ) + >.9 ( 7>>> ) ?112>   112>?112> Ke (7) >.9 x + >.;  y + >. >.9 ( 17>> )+ >.; ( 3>> )+ >.< ( 7>>> )?1;2>   1;2>?1;2> Ke (9) >.1 x + >.7 y + >.1 z ? >.1 ( 17>> )+ >.7 ( 3>> )+ >.1 (7>>> )?   ? ^jr taetj, sk puklke prjlui`r 17>> iao`sas t`pj A, 3>> t`pjs G y 7>>> t`pj I 7. [e iketrj lk l`vkrs`ùe l`vkrs`ùe t`kek iapai`lal iapai`lal par paraa 1>1 oksas, fas oksas iuk iuketae etae ije 1 ⑮ 2

 

<  x

1 7

+ 2 y + 3 z ?;;7 ② 1

1

3

9

 x +  y +  z ?9; ⑧

Iafiufaojs fjs lktkro`eaetks  1

1

1

<

2

3

/

1 9

1>1

1

1

| x|? ;;7

2

3

| | | |

|s|? 1 / 7

| y|?

| y|?

1 3

1.12

| | | |

/ ?

9;

1 3

/

1 9

 1

1>1

1

<

;;7

3

1 7

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9;

1 9

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;;7

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1 3

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?;2

?9=.99

?7 pksjs. ^jr jtra partk, vkelk 17 rasijs lk v`tao`ea A, < lk v`tao`ea I y 1; lk v`tao`ea L pjr ue tjtaf lk 722 pksjs. Keiuketra kf ijstj ijrrkspjel`ketk a iala rasij lk fas v`tao`eas A, I y L. ;. [e fagjra fagjratjr tjr`st `staa t`k t`kek ek trks trks sjf sjfui` ui`jek jekss quk ije ijet`k t`keke eke i`k i`krtj rtj ái`lj. ái`lj. Fa pr`okr pr`okraa sjfui`ùe ijet`kek 1>% lk sustaei`a ái`la, fa skmuela 9>% y fa tkrikra ;>%. Lkska ut`f`zar fas trks sjfui`jeks para jgtkekr uea okzifa lk 2> f`trjs quk ijetkema 9>% lk ái`lj, ut`f`zaelj trks vkiks oás sjfui`ùe lk fa sjfui`ùe lk ;>% quk fa lk 9>% ºIuáetjs f`trjs lk iala sjfui`ùe lkgk usar: 2. [ea oudkr ijoprù trks ifasks l`krketks l lkk aii`jeks pjr $7> >>>. [ea lk kffas pama ue 2% aeuaf lk `etkrksks, jtra pama ue =%, y fa jtra ue 3% aeuaf. Af b`eaf lkf pr`okr añj, fa suoa lk fjs `etkrksks lk fas aii`jeks af 2% y af =% ks lk $0, y fa suoa lk fjs `etkrksks lk fas aii`jeks af 2% y af 3% ks lk $=7>. ºIuáetj `ev`rt`ù ke iala uea lk fas aii`jeks: =. [e ijok ijokri ri`a `aet etkk vk vkel elkk tr trks ks t` t`pj pjss lk quksj quksjs, s, lksi lksirk rkoa oalj lj,, sko` sko`-l -lks ksir irko koal aljj y ijstk stkñj, ñj, fjs prki` ki`js pjr h`fùmraoj sje $17 >>>, $1> >>> y $ 0 >>> rkspkit`vaoketk. Yk sagk quk ue lïa vkel`ù ke tjtaf > y iaet`lal lk quksj sko`-lksirkoalj ks kf ljgfk quk fa vkel`la lk quksj lksirkoalj. ºIuáetjs h`fjs lk iala t`pj lk quksj sk vkel`ù:   3. Ke uea ckfalkrïa ckfalkrïa pjr ue ckfa ckfalj, lj, ljs dumj dumjss y iuatrj oaft oaftkalas kalas sk pama pamarje rje 9;₦. Jtr Jtrjj lïa pjr iuatrj ckfaljs, iuatrj dumjs y uea oaftkala ijgrarje 9