153:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000
v  = (6, 2):@0.477618:0.525349:0.522475:0.525349:0.522475:0.514406:0.477618:0.514406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.290410:0.602581:0.295973:0.602581:0.295973:0.591638:0.290410:0.591638:0.000000
1:@0.321190:0.602581:0.326753:0.602581:0.326753:0.591638:0.321190:0.591638:0.000000
2:@0.360747:0.602581:0.366310:0.602581:0.366310:0.591638:0.360747:0.591638:0.000000
3:@0.400305:0.602581:0.405868:0.602581:0.405868:0.591638:0.400305:0.591638:0.000000
4:@0.439862:0.602581:0.445425:0.602581:0.445425:0.591638:0.439862:0.591638:0.000000
5:@0.479420:0.602581:0.484983:0.602581:0.484983:0.591638:0.479420:0.591638:0.000000
6:@0.518977:0.602581:0.524541:0.602581:0.524541:0.591638:0.518977:0.591638:0.000000
–3:@0.159657:0.584777:0.171901:0.584777:0.171901:0.573835:0.159657:0.573835:0.000000:0.000000
–2:@0.199215:0.584777:0.211459:0.584777:0.211459:0.573835:0.199215:0.573835:0.000000:0.000000
–1:@0.238772:0.584777:0.251016:0.584777:0.251016:0.573835:0.238772:0.573835:0.000000:0.000000
1:@0.271121:0.562789:0.276685:0.562789:0.276685:0.551846:0.271121:0.551846:0.000000
2:@0.271121:0.533100:0.276685:0.533100:0.276685:0.522158:0.271121:0.522158:0.000000
–1:@0.291277:0.621949:0.303521:0.621949:0.303521:0.611007:0.291277:0.611007:0.000000:0.000000
y:@0.271267:0.508854:0.276491:0.508854:0.276491:0.497912:0.271267:0.497912:0.000000
x:@0.554373:0.602576:0.559434:0.602576:0.559434:0.591634:0.554373:0.591634:0.000000
v  = (–3, –1):@0.152701:0.634197:0.210919:0.634197:0.210919:0.623255:0.152701:0.623255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u = (3, 1):@0.360308:0.554933:0.403282:0.554933:0.403282:0.543991:0.360308:0.543991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.481919:0.526255:0.485162:0.526255:0.485162:0.519875:0.481919:0.519875:0.000000
2:@0.157505:0.635018:0.160748:0.635018:0.160748:0.628639:0.157505:0.628639:0.000000
Ejercicios resueltos:@0.108233:0.096570:0.238888:0.096570:0.238888:0.079783:0.108233:0.079783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108233:0.120890:0.120505:0.120890:0.120505:0.104176:0.108233:0.104176:0.000000:0.000000
   Sean :@0.120506:0.120674:0.169478:0.120674:0.169478:0.104176:0.120506:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.187566:0.121310:0.198142:0.121310:0.198142:0.105029:0.187566:0.105029:0.000000
(3,2),  :@0.200859:0.120674:0.246883:0.120674:0.246883:0.104176:0.200859:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.174523:0.120790:0.183732:0.120790:0.183732:0.104321:0.174523:0.104321:0.000000
=−:@0.265230:0.121310:0.298000:0.121310:0.298000:0.105029:0.265230:0.105029:0.000000:0.000000
v:@0.252187:0.120790:0.259970:0.120790:0.259970:0.104321:0.252187:0.104321:0.000000
(2,1).   Entonces :@0.279313:0.120674:0.408051:0.120674:0.408051:0.104176:0.279313:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+=:@0.424934:0.121310:0.460478:0.121310:0.460478:0.105029:0.424934:0.105029:0.000000:0.000000
(1,3).   En  la  figura :@0.463195:0.120674:0.599911:0.120674:0.599911:0.104176:0.463195:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.413086:0.120790:0.445047:0.120790:0.445047:0.104321:0.413086:0.104321:0.000000:0.000000
3.20. se muestran los vectores  ,   y   +  .:@0.131678:0.138025:0.447669:0.138025:0.447669:0.121527:0.131678:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.347365:0.138140:0.377384:0.138140:0.377384:0.121672:0.347365:0.121672:0.000000:0.000000:0.000000
u:@0.400520:0.138140:0.409729:0.138140:0.409729:0.121672:0.400520:0.121672:0.000000
v:@0.434952:0.138140:0.442735:0.138140:0.442735:0.121672:0.434952:0.121672:0.000000
2.:@0.108235:0.172148:0.120507:0.172148:0.120507:0.155433:0.108235:0.155433:0.000000:0.000000
   Sean :@0.120508:0.171930:0.169480:0.171930:0.169480:0.155433:0.120508:0.155433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.217700:0.162621:0.226196:0.162621:0.226196:0.146124:0.217700:0.146124:0.000000
2:@0.217072:0.182934:0.225568:0.182934:0.225568:0.166436:0.217072:0.166436:0.000000
,:@0.229536:0.171931:0.232291:0.171931:0.232291:0.155433:0.229536:0.155433:0.000000
2.  Entonces :@0.265967:0.171931:0.353335:0.171933:0.353335:0.155435:0.265967:0.155433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.169998:0.172569:0.182155:0.172569:0.186927:0.156288:0.174771:0.156288:0.000000
β:@0.235019:0.172569:0.245595:0.172569:0.250368:0.156288:0.239791:0.156288:0.000000
=−:@0.188908:0.172569:0.213933:0.172569:0.213933:0.156288:0.188908:0.156288:0.000000:0.000000
=:@0.251943:0.172569:0.262520:0.172569:0.262520:0.156288:0.251943:0.156288:0.000000
ααα:@0.353847:0.172569:0.371700:0.172569:0.376472:0.156288:0.358620:0.156288:0.000000:0.000000:0.000000
βββ:@0.470845:0.172569:0.487118:0.172569:0.491890:0.156288:0.475618:0.156288:0.000000:0.000000:0.000000
(((:@0.509342:0.175603:0.521454:0.175603:0.521454:0.154113:0.509342:0.154113:0.000000:0.000000:0.000000
))):@0.551899:0.175603:0.564010:0.175603:0.564010:0.154113:0.551899:0.154113:0.000000:0.000000:0.000000
−−−:@0.396420:0.172569:0.412694:0.172569:0.412694:0.156288:0.396420:0.156288:0.000000:0.000000:0.000000
−−−:@0.428361:0.172569:0.444635:0.172569:0.444635:0.156288:0.428361:0.156288:0.000000:0.000000:0.000000
=−=−=−:@0.496040:0.172569:0.532314:0.172569:0.532314:0.156288:0.496040:0.156288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
===:@0.377469:0.171933:0.393973:0.171933:0.393973:0.155435:0.377469:0.155435:0.000000:0.000000:0.000000
33 3:@0.409612:0.163054:0.423795:0.163055:0.423795:0.146557:0.409612:0.146556:0.000000:0.000000:0.000000:0.000000
22 2:@0.409400:0.183325:0.423584:0.183326:0.423584:0.166829:0.409400:0.166827:0.000000:0.000000:0.000000:0.000000
,1:@0.421903:0.171932:0.448566:0.171932:0.448566:0.155434:0.421903:0.155434:0.000000:0.000000
4, 2 24, 2:@0.526456:0.171932:0.556990:0.171933:0.556990:0.155435:0.526456:0.155434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u uu:@0.367363:0.172047:0.382270:0.172048:0.382270:0.155580:0.367363:0.155578:0.000000:0.000000:0.000000:0.000000
y v vy v:@0.459663:0.172047:0.496907:0.172048:0.496907:0.155580:0.459663:0.155578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,1,1:@0.422205:0.171933:0.454254:0.171933:0.454254:0.155435:0.422205:0.155435:0.000000:0.000000:0.000000:0.000000
4,:@0.526757:0.171933:0.539415:0.171933:0.539415:0.155435:0.526757:0.155435:0.000000:0.000000
y:@0.459965:0.172048:0.467652:0.172048:0.467652:0.155580:0.459965:0.155580:0.000000
 :@0.108233:0.203540:0.112375:0.203540:0.112375:0.187042:0.108233:0.187042:0.000000
En la figura 3.21. se muestran los vectores  , :@0.131680:0.203540:0.449493:0.203540:0.449493:0.187042:0.131680:0.187042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v ,  u:@0.429665:0.203656:0.495074:0.203656:0.495074:0.187187:0.429665:0.187187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.471563:0.204089:0.483720:0.204089:0.483720:0.185249:0.471563:0.185249:0.000000
 y :@0.498797:0.203540:0.514903:0.203540:0.514903:0.187042:0.498797:0.187042:0.000000:0.000000:0.000000
β:@0.514903:0.204089:0.525479:0.204089:0.525479:0.185249:0.514903:0.185249:0.000000
v:@0.527886:0.203656:0.535669:0.203656:0.535669:0.187187:0.527886:0.187187:0.000000
. :@0.537423:0.203540:0.544320:0.203540:0.544320:0.187042:0.537423:0.187042:0.000000:0.000000
Vectores colineales:@0.108233:0.239639:0.261192:0.239639:0.261192:0.221956:0.108233:0.221956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.263937:0.188317:0.263937:0.188317:0.246991:0.108233:0.246991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   :@0.108233:0.280825:0.172406:0.280825:0.172406:0.264327:0.108233:0.264327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.145203:0.280941:0.168264:0.280941:0.168264:0.264472:0.145203:0.264472:0.000000:0.000000:0.000000
:@0.171577:0.280608:0.187625:0.280608:0.187625:0.265961:0.171577:0.265961:0.000000
R:@0.187626:0.279856:0.201536:0.279856:0.201536:0.266410:0.187626:0.266410:0.000000
2:@0.201559:0.274472:0.206512:0.274472:0.206512:0.264854:0.201559:0.264854:0.000000
 con  ≠ 0. Se dice que los vectores   y   son colineales :@0.206513:0.280825:0.599894:0.280825:0.599894:0.264327:0.206513:0.264327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u :@0.240092:0.280941:0.253443:0.280941:0.253443:0.264472:0.240092:0.264472:0.000000:0.000000
u:@0.452195:0.280941:0.461404:0.280941:0.461404:0.264472:0.452195:0.264472:0.000000
v:@0.481999:0.280941:0.489782:0.280941:0.489782:0.264472:0.481999:0.264472:0.000000
si y solo si existe un número real :@0.108226:0.298176:0.339867:0.298176:0.339867:0.281678:0.108226:0.281678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.339867:0.298725:0.350444:0.298725:0.350444:0.279885:0.339867:0.279885:0.000000
:@0.350444:0.297959:0.366492:0.297959:0.366492:0.283312:0.350444:0.283312:0.000000
R:@0.366496:0.297207:0.380406:0.297207:0.380406:0.283760:0.366496:0.283760:0.000000
, tal que  = :@0.380406:0.298176:0.470619:0.298176:0.470619:0.281678:0.380406:0.281678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.443001:0.298292:0.450784:0.298292:0.450784:0.281823:0.443001:0.281823:0.000000
λ:@0.470619:0.298725:0.481196:0.298725:0.481196:0.279885:0.470619:0.279885:0.000000
u:@0.483343:0.298292:0.492551:0.298292:0.492551:0.281823:0.483343:0.281823:0.000000
. :@0.493595:0.298176:0.500492:0.298176:0.500492:0.281678:0.493595:0.281678:0.000000:0.000000
En la definición precedente, si  > 0, los vectores   y   tienen la mis-:@0.108232:0.322655:0.595759:0.322654:0.595759:0.306157:0.108232:0.306157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ :@0.321073:0.323204:0.336466:0.323204:0.336466:0.304364:0.321073:0.304364:0.000000:0.000000
u:@0.454306:0.322770:0.463515:0.322770:0.463515:0.306301:0.454306:0.306301:0.000000
v:@0.484857:0.322770:0.492640:0.322770:0.492640:0.306301:0.484857:0.306301:0.000000
ma dirección y sentido. También, si  < 0, los vectores   y   tienen la :@0.108232:0.340005:0.599923:0.340005:0.599923:0.323507:0.108232:0.323507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ :@0.356326:0.340554:0.371719:0.340554:0.371719:0.321714:0.356326:0.321714:0.000000:0.000000
u:@0.488931:0.340121:0.498140:0.340121:0.498140:0.323652:0.488931:0.323652:0.000000
v:@0.519246:0.340121:0.527030:0.340121:0.527030:0.323652:0.519246:0.323652:0.000000
misma dirección, pero son de sentidos opuestos. En la figura 3.22. se :@0.108235:0.357356:0.599878:0.357356:0.599878:0.340858:0.108235:0.340858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muestran dos vectores colineales a   para los dos casos  > 0 y  < 0.:@0.108235:0.374706:0.595767:0.374706:0.595767:0.358209:0.108235:0.358209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.357721:0.374822:0.366930:0.374822:0.366930:0.358353:0.357721:0.358353:0.000000
λ :@0.503174:0.375256:0.518567:0.375256:0.518567:0.356416:0.503174:0.356416:0.000000:0.000000
λ :@0.555522:0.375256:0.570915:0.375256:0.570915:0.356416:0.555522:0.356416:0.000000:0.000000
Ejercicio resuelto:@0.108221:0.399561:0.226200:0.399561:0.226200:0.382775:0.108221:0.382775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108221:0.425761:0.120493:0.425761:0.120493:0.409047:0.108221:0.409047:0.000000:0.000000
   Sea  =3,1:@0.120492:0.425544:0.212490:0.425550:0.212490:0.409053:0.120492:0.409047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.  Entonces  =:@0.278223:0.425550:0.383766:0.424293:0.383766:0.407796:0.278223:0.409053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.233718:0.426187:0.244294:0.426187:0.249067:0.409906:0.238490:0.409906:0.000000
( ):@0.184415:0.428486:0.217955:0.428486:0.217955:0.406507:0.184415:0.406507:0.000000:0.000000:0.000000
∈:@0.249801:0.426187:0.263537:0.426187:0.263537:0.409906:0.249801:0.409906:0.000000
u:@0.163319:0.425666:0.172528:0.425666:0.172528:0.409197:0.163319:0.409197:0.000000
y:@0.222637:0.425666:0.230324:0.425666:0.230324:0.409197:0.222637:0.409197:0.000000
3,1:@0.441638:0.424293:0.462599:0.424293:0.462599:0.407796:0.441638:0.407796:0.000000:0.000000:0.000000
3,:@0.491593:0.424293:0.516176:0.424293:0.516176:0.407796:0.491593:0.407796:0.000000:0.000000
λ:@0.382109:0.424929:0.392685:0.424929:0.397458:0.408649:0.386881:0.408649:0.000000
λ:@0.420697:0.424929:0.431274:0.424929:0.436046:0.408649:0.425470:0.408649:0.000000
λλ:@0.499068:0.424929:0.526926:0.424929:0.531698:0.408649:0.503841:0.408649:0.000000:0.000000
( ) (:@0.434523:0.427228:0.490874:0.427228:0.490874:0.405249:0.434523:0.405249:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.530310:0.427228:0.536725:0.427228:0.536725:0.405249:0.530310:0.405249:0.000000
=:@0.407510:0.424929:0.418086:0.424929:0.418086:0.408649:0.407510:0.408649:0.000000
=:@0.470854:0.424929:0.481430:0.424929:0.481430:0.408649:0.470854:0.408649:0.000000
v:@0.363277:0.424409:0.371060:0.424409:0.371060:0.407940:0.363277:0.407940:0.000000
u:@0.394120:0.424409:0.403329:0.424409:0.403329:0.407940:0.394120:0.407940:0.000000
 es coli-:@0.540112:0.425551:0.595748:0.425551:0.595748:0.409053:0.540112:0.409053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
neal a  . Para  = 2, se obtiene :@0.131689:0.444782:0.359237:0.444787:0.359237:0.428290:0.131689:0.428284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.179856:0.444903:0.189065:0.444903:0.189065:0.428434:0.179856:0.428434:0.000000
λ :@0.234786:0.445337:0.250179:0.445337:0.250179:0.426497:0.234786:0.426497:0.000000:0.000000
6,2  y para  = –1, se tiene :@0.399860:0.443530:0.599906:0.444787:0.599906:0.428290:0.399860:0.427032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.369393:0.445749:0.374310:0.445749:0.374310:0.436200:0.369393:0.436200:0.000000
( ):@0.392322:0.446465:0.429465:0.446465:0.429465:0.424486:0.392322:0.424486:0.000000:0.000000:0.000000
=:@0.378711:0.444166:0.389287:0.444166:0.389287:0.427885:0.378711:0.427885:0.000000
v:@0.361950:0.443646:0.369733:0.443646:0.369733:0.427177:0.361950:0.427177:0.000000
λ :@0.483995:0.445337:0.499388:0.445337:0.499388:0.426497:0.483995:0.426497:0.000000:0.000000
3, 1.  En la figura 3.23. se muestran los vectores :@0.184038:0.462767:0.543631:0.464025:0.543631:0.447527:0.184038:0.446269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.141999:0.464985:0.146917:0.464985:0.146917:0.455437:0.141999:0.455437:0.000000
(:@0.166081:0.465702:0.172496:0.465702:0.172496:0.443723:0.166081:0.443723:0.000000
):@0.215650:0.465702:0.222066:0.465702:0.222066:0.443723:0.215650:0.443723:0.000000
=− −:@0.152469:0.463403:0.208281:0.463403:0.208281:0.447122:0.152469:0.447122:0.000000:0.000000:0.000000:0.000000
v:@0.134090:0.462882:0.141874:0.462882:0.141874:0.446414:0.134090:0.446414:0.000000
y:@0.565404:0.464024:0.573226:0.464024:0.573226:0.447526:0.565404:0.447526:0.000000
1:@0.555353:0.466243:0.560270:0.466243:0.560270:0.456694:0.555353:0.456694:0.000000
2:@0.587656:0.466243:0.592574:0.466243:0.592574:0.456694:0.587656:0.456694:0.000000
v:@0.547918:0.464140:0.555701:0.464140:0.555701:0.447671:0.547918:0.447671:0.000000
v  :@0.579744:0.464140:0.599910:0.464140:0.599910:0.447671:0.579744:0.447671:0.000000:0.000000:0.000000
colineales a  .  :@0.131687:0.481375:0.239137:0.481375:0.239137:0.464877:0.131687:0.464877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.218718:0.481490:0.227927:0.481490:0.227927:0.465022:0.218718:0.465022:0.000000
2.:@0.108230:0.680431:0.120502:0.680431:0.120502:0.663717:0.108230:0.663717:0.000000:0.000000
   Los  vectores  =(1, 2),(1, 3)  no son colineales. Sin embargo,  :@0.120503:0.680214:0.599908:0.680209:0.599908:0.663712:0.120503:0.663717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.235667:0.680325:0.244876:0.680325:0.244876:0.663856:0.235667:0.663856:0.000000
v:@0.297277:0.680325:0.305060:0.680325:0.305060:0.663856:0.297277:0.663856:0.000000
supongamos que lo son. Entonces, existe :@0.131685:0.697560:0.424877:0.697560:0.424877:0.681062:0.131685:0.681062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.424877:0.697676:0.436494:0.697676:0.436494:0.681207:0.424877:0.681207:0.000000:0.000000
 :@0.436494:0.697343:0.457358:0.697343:0.457358:0.682696:0.436494:0.682696:0.000000:0.000000
R:@0.457365:0.696591:0.471274:0.696591:0.471274:0.683144:0.457365:0.683144:0.000000
 tal que :@0.471274:0.697560:0.528704:0.697560:0.528704:0.681062:0.471274:0.681062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.  :@0.577017:0.697434:0.588121:0.697560:0.588121:0.681062:0.577017:0.680937:0.000000:0.000000:0.000000
=:@0.544093:0.698070:0.554669:0.698070:0.554669:0.681790:0.544093:0.681790:0.000000
v:@0.531108:0.697550:0.538891:0.697550:0.538891:0.681081:0.531108:0.681081:0.000000
xu:@0.559274:0.697550:0.575707:0.697550:0.575707:0.681081:0.559274:0.681081:0.000000:0.000000
Luego,:@0.131670:0.736526:0.177635:0.736526:0.177635:0.720029:0.131670:0.720029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(1,3):@0.258644:0.736525:0.291511:0.736525:0.291511:0.720027:0.258644:0.720027:0.000000:0.000000:0.000000:0.000000:0.000000
(1, 2) (, 2)   :@0.318270:0.736525:0.442062:0.736525:0.442062:0.720027:0.318270:0.720027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 1 1:@0.453551:0.725883:0.461256:0.725883:0.461256:0.709386:0.453551:0.709386:0.000000:0.000000:0.000000:0.000000:0.000000
, ,,:@0.488267:0.725883:0.490231:0.725883:0.490231:0.709386:0.488267:0.709386:0.000000:0.000000:0.000000:0.000000
32 . .:@0.454341:0.747572:0.500587:0.747567:0.500587:0.731069:0.454341:0.731074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.197188:0.737161:0.110186:0.737161:0.110186:0.720880:0.197188:0.720880:0.000000
= =:@0.294767:0.737161:0.109386:0.737161:0.109386:0.720880:0.294767:0.720880:0.000000:0.000000:0.000000
= = =:@0.354817:0.737161:0.364599:0.737161:0.364599:0.720880:0.354817:0.720880:0.000000:0.000000:0.000000:0.000000:0.000000
= = =:@0.463608:0.726519:0.473386:0.726514:0.473386:0.710234:0.463608:0.710239:0.000000:0.000000:0.000000:0.000000:0.000000
= = =:@0.465958:0.748208:0.475736:0.748203:0.475736:0.731922:0.465958:0.731927:0.000000:0.000000:0.000000:0.000000:0.000000
v v v:@0.184203:0.736641:0.191194:0.736641:0.191194:0.720172:0.184203:0.720172:0.000000:0.000000:0.000000:0.000000:0.000000
xu xu xu:@0.212369:0.736641:0.228010:0.736641:0.228010:0.720172:0.212369:0.720172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x x:@0.309948:0.736641:0.316630:0.736641:0.316630:0.720172:0.309948:0.720172:0.000000:0.000000:0.000000:0.000000:0.000000
xx:@0.375546:0.736641:0.408721:0.736641:0.408721:0.720172:0.375546:0.720172:0.000000:0.000000
x x x:@0.478789:0.725999:0.485467:0.725994:0.485467:0.709525:0.478789:0.709530:0.000000:0.000000:0.000000:0.000000:0.000000
x x x:@0.489885:0.747687:0.496564:0.747682:0.496564:0.731214:0.489885:0.731219:0.000000:0.000000:0.000000:0.000000:0.000000
   (1(1:@0.230273:0.736525:0.271108:0.736525:0.271108:0.720027:0.230273:0.720027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,3:@0.270520:0.736525:0.285354:0.736525:0.285354:0.720027:0.270520:0.720027:0.000000:0.000000
):@0.284757:0.736525:0.290710:0.736525:0.290710:0.720027:0.284757:0.720027:0.000000
((:@0.317470:0.736525:0.323433:0.736525:0.323433:0.720027:0.317470:0.720027:0.000000:0.000000
1,:@0.322247:0.736525:0.332901:0.736525:0.332901:0.720027:0.322247:0.720027:0.000000:0.000000
2):@0.336484:0.736525:0.350760:0.736525:0.350760:0.720027:0.336484:0.720027:0.000000:0.000000
(,:@0.368060:0.736525:0.386998:0.736525:0.386998:0.720027:0.368060:0.720027:0.000000:0.000000
2):@0.390563:0.736525:0.414317:0.736525:0.414317:0.720027:0.390563:0.720027:0.000000:0.000000
3232:@0.453541:0.747572:0.487708:0.747572:0.487708:0.731074:0.453541:0.731074:0.000000:0.000000:0.000000:0.000000
.:@0.497832:0.747572:0.500587:0.747572:0.500587:0.731074:0.497832:0.731074:0.000000
= =:@0.293967:0.737161:0.109392:0.737161:0.109392:0.720880:0.293967:0.720880:0.000000:0.000000:0.000000
xx:@0.374746:0.736636:0.407921:0.736636:0.407921:0.720167:0.374746:0.720167:0.000000:0.000000
,3:@0.270530:0.736525:0.285365:0.736525:0.285365:0.720027:0.270530:0.720027:0.000000:0.000000
):@0.284767:0.736525:0.290720:0.736525:0.290720:0.720027:0.284767:0.720027:0.000000
1,:@0.322257:0.736525:0.332911:0.736525:0.332911:0.720027:0.322257:0.720027:0.000000:0.000000
2):@0.336495:0.736525:0.350770:0.736525:0.350770:0.720027:0.336495:0.720027:0.000000:0.000000
(,:@0.368070:0.736525:0.387008:0.736525:0.387008:0.720027:0.368070:0.720027:0.000000:0.000000
2):@0.390572:0.736525:0.414326:0.736525:0.414326:0.720027:0.390572:0.720027:0.000000:0.000000
=:@0.293973:0.737161:0.206971:0.737161:0.206971:0.720880:0.293973:0.720880:0.000000
xx:@0.374754:0.736641:0.407928:0.736641:0.407928:0.720172:0.374754:0.720172:0.000000:0.000000
 :@0.108231:0.761005:0.112373:0.761005:0.112373:0.744507:0.108231:0.744507:0.000000
De la primera igualdad, se obtiene   = 1. Al reemplazar   = 1 en la :@0.108231:0.778355:0.599915:0.778355:0.599915:0.761858:0.108231:0.761858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.363378:0.778471:0.370853:0.778471:0.370853:0.762002:0.363378:0.762002:0.000000
x:@0.516593:0.778471:0.524068:0.778471:0.524068:0.762002:0.516593:0.762002:0.000000
segunda igualdad, resulta 3 = 2, lo que es un :@0.108231:0.795706:0.429801:0.795706:0.429801:0.779209:0.108231:0.779209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
absurdo:@0.430398:0.795923:0.490562:0.795923:0.490562:0.779209:0.430398:0.779209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Este hecho se :@0.490492:0.795706:0.599917:0.795706:0.599917:0.779209:0.490492:0.779209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
produce por haber supuesto que los vectores  ,  son colineales.  :@0.108231:0.813057:0.599916:0.813057:0.599916:0.796559:0.108231:0.796559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.453780:0.813173:0.478998:0.813173:0.478998:0.796704:0.453780:0.796704:0.000000:0.000000
Lo correcto es que  ,  no son colineales.:@0.108247:0.830408:0.406436:0.830408:0.406436:0.813910:0.108247:0.813910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.245988:0.830523:0.271206:0.830523:0.271206:0.814055:0.245988:0.814055:0.000000:0.000000
Teorema:@0.108231:0.855349:0.175176:0.855349:0.175176:0.838404:0.108231:0.838404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.108231:0.880248:0.146030:0.880248:0.146030:0.863750:0.108231:0.863750:0.000000:0.000000:0.000000:0.000000:0.000000
(, ),:@0.178122:0.880245:0.217423:0.880245:0.217423:0.863747:0.178122:0.863747:0.000000:0.000000:0.000000:0.000000:0.000000
(, )  dos vectores de :@0.247863:0.880245:0.414827:0.880245:0.414827:0.863747:0.247863:0.863747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.164092:0.880881:0.104929:0.880881:0.104929:0.864600:0.164092:0.864600:0.000000
=:@0.233832:0.880881:0.174669:0.880881:0.174669:0.864600:0.233832:0.864600:0.000000
u:@0.150690:0.880360:0.159899:0.880360:0.159899:0.863892:0.150690:0.863892:0.000000
a bv:@0.184096:0.880360:0.228618:0.880360:0.228618:0.863892:0.184096:0.863892:0.000000:0.000000:0.000000:0.000000
cd:@0.253817:0.880360:0.278438:0.880360:0.278438:0.863892:0.253817:0.863892:0.000000:0.000000
R:@0.417340:0.879276:0.431249:0.879276:0.431249:0.865829:0.417340:0.865829:0.000000
2:@0.431249:0.873893:0.436203:0.873893:0.436203:0.864275:0.431249:0.864275:0.000000
 con :@0.436203:0.880245:0.473953:0.880245:0.473953:0.863747:0.436203:0.863747:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.507165:0.880619:0.515661:0.880619:0.515661:0.864122:0.507165:0.864122:0.000000
 :@0.480540:0.872450:0.515295:0.870353:0.515295:0.852844:0.480540:0.854940:0.000000:0.000000:0.000000
≠:@0.492581:0.881255:0.503157:0.881255:0.503157:0.864975:0.492581:0.864975:0.000000
u:@0.479172:0.880735:0.488381:0.880735:0.488381:0.864266:0.479172:0.864266:0.000000
. Entonces,  :@0.518348:0.880245:0.599906:0.880245:0.599906:0.863747:0.518348:0.863747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  son colineales si y solo si :@0.124513:0.897595:0.331067:0.897595:0.331067:0.881098:0.124513:0.881098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
uv:@0.110372:0.897711:0.144067:0.897711:0.144067:0.881242:0.110372:0.881242:0.000000:0.000000
0.:@0.402735:0.897595:0.413909:0.897595:0.413909:0.881098:0.402735:0.881098:0.000000:0.000000
−:@0.352954:0.898232:0.363530:0.898232:0.363530:0.881951:0.352954:0.881951:0.000000
=:@0.388286:0.898232:0.398863:0.898232:0.398863:0.881951:0.388286:0.881951:0.000000
ac bd:@0.334055:0.897711:0.384626:0.897711:0.384626:0.881242:0.334055:0.881242:0.000000:0.000000:0.000000:0.000000:0.000000
La Demostración. se deja como investigación para el estudiante.:@0.108231:0.922074:0.559995:0.922074:0.559995:0.905577:0.108231:0.905577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.526926:0.650167:0.538406:0.650167:0.538406:0.640142:0.526926:0.640142:0.000000
 Figura 3.23.:@0.538406:0.650875:0.595766:0.650875:0.595766:0.639398:0.538406:0.639398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2:@0.648670:0.197458:0.658976:0.197458:0.658976:0.188248:0.648670:0.188248:0.000000:0.000000
–1:@0.681967:0.197458:0.692273:0.197458:0.692273:0.188248:0.681967:0.188248:0.000000:0.000000
1:@0.751360:0.197458:0.756043:0.197458:0.756043:0.188248:0.751360:0.188248:0.000000
2:@0.784657:0.197458:0.789339:0.197458:0.789339:0.188248:0.784657:0.188248:0.000000
3:@0.817953:0.197458:0.822636:0.197458:0.822636:0.188248:0.817953:0.188248:0.000000
x:@0.842127:0.193491:0.846387:0.193491:0.846387:0.184281:0.842127:0.184281:0.000000
3:@0.707240:0.114159:0.711923:0.114159:0.711923:0.104949:0.707240:0.104949:0.000000
1:@0.707240:0.164131:0.711923:0.164131:0.711923:0.154920:0.707240:0.154920:0.000000
0:@0.713001:0.194372:0.717684:0.194372:0.717684:0.185161:0.713001:0.185161:0.000000
y:@0.710284:0.095651:0.714682:0.095651:0.714682:0.086441:0.710284:0.086441:0.000000
2:@0.707251:0.139149:0.711933:0.139149:0.711933:0.129939:0.707251:0.129939:0.000000
u:@0.690278:0.137350:0.695500:0.137350:0.695500:0.128140:0.690278:0.128140:0.000000
v:@0.644863:0.172829:0.649302:0.172829:0.649302:0.163618:0.644863:0.163618:0.000000
u:@0.782731:0.164685:0.787953:0.164685:0.787953:0.155475:0.782731:0.155475:0.000000
v:@0.790367:0.121704:0.794807:0.121704:0.794807:0.112494:0.790367:0.112494:0.000000
u + v:@0.741613:0.154544:0.763884:0.154544:0.763884:0.145333:0.741613:0.145333:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.787313:0.221335:0.798794:0.221335:0.798794:0.211311:0.787313:0.211311:0.000000
 Figura 3.20.:@0.798794:0.222043:0.856154:0.222043:0.856154:0.210566:0.798794:0.210566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–4:@0.642877:0.328843:0.650932:0.328843:0.650932:0.321645:0.642877:0.321645:0.000000:0.000000
–3:@0.668899:0.328843:0.676953:0.328843:0.676953:0.321645:0.668899:0.321645:0.000000:0.000000
–2:@0.694920:0.328843:0.702975:0.328843:0.702975:0.321645:0.694920:0.321645:0.000000:0.000000
–1:@0.720942:0.328843:0.728996:0.328843:0.728996:0.321645:0.720942:0.321645:0.000000:0.000000
1:@0.775174:0.328843:0.778833:0.328843:0.778833:0.321645:0.775174:0.321645:0.000000
2:@0.801195:0.328843:0.804855:0.328843:0.804855:0.321645:0.801195:0.321645:0.000000
3:@0.827217:0.328843:0.830876:0.328843:0.830876:0.321645:0.827217:0.321645:0.000000
x:@0.845192:0.325743:0.848521:0.325743:0.848521:0.318545:0.845192:0.318545:0.000000
3:@0.740693:0.263744:0.744353:0.263744:0.744353:0.256546:0.740693:0.256546:0.000000
1:@0.740693:0.302797:0.744353:0.302797:0.744353:0.295599:0.740693:0.295599:0.000000
0:@0.751622:0.325743:0.755282:0.325743:0.755282:0.318545:0.751622:0.318545:0.000000
–1:@0.755934:0.341856:0.763989:0.341856:0.763989:0.334658:0.755934:0.334658:0.000000:0.000000
y:@0.743312:0.247215:0.746748:0.247215:0.746748:0.240017:0.743312:0.240017:0.000000
2:@0.740693:0.283274:0.744353:0.283274:0.744353:0.276076:0.740693:0.276076:0.000000
v:@0.683949:0.292122:0.687419:0.292122:0.687419:0.284924:0.683949:0.284924:0.000000
v:@0.722076:0.308453:0.725546:0.308453:0.725546:0.301255:0.722076:0.301255:0.000000
u:@0.807731:0.298533:0.811812:0.298533:0.811812:0.291335:0.807731:0.291335:0.000000
β:@0.678446:0.291705:0.682981:0.291705:0.682981:0.283626:0.678446:0.283626:0.000000
u:@0.730968:0.348477:0.735049:0.348477:0.735049:0.341279:0.730968:0.341279:0.000000
α:@0.724336:0.348550:0.729548:0.348550:0.729548:0.340472:0.724336:0.340472:0.000000
p:@0.787313:0.369415:0.798794:0.369415:0.798794:0.359391:0.787313:0.359391:0.000000
 :@0.798794:0.370123:0.801675:0.370123:0.801675:0.358646:0.798794:0.358646:0.000000
Figura 3.21.:@0.801675:0.370123:0.856154:0.370123:0.856154:0.358646:0.801675:0.358646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.721423:0.403403:0.727059:0.403403:0.727059:0.391598:0.721423:0.391598:0.000000
x:@0.838175:0.502680:0.843635:0.502680:0.843635:0.490875:0.838175:0.490875:0.000000
0:@0.725324:0.502680:0.731326:0.502680:0.731326:0.490875:0.725324:0.490875:0.000000
u:@0.701982:0.463951:0.708674:0.463951:0.708674:0.452147:0.701982:0.452147:0.000000
v =  u:@0.781562:0.522380:0.815241:0.522380:0.815241:0.510575:0.781562:0.510575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
< 0:@0.766660:0.504566:0.783147:0.504566:0.783147:0.492965:0.766660:0.492965:0.000000:0.000000:0.000000
 :@0.783147:0.504831:0.786182:0.504831:0.786182:0.493026:0.783147:0.493026:0.000000
λ:@0.801111:0.522563:0.808549:0.522563:0.808549:0.511114:0.801111:0.511114:0.000000
v =  u:@0.645434:0.422362:0.679099:0.422362:0.679099:0.410557:0.645434:0.410557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.664969:0.422545:0.672407:0.422545:0.672407:0.411096:0.664969:0.411096:0.000000
> 0:@0.685575:0.440928:0.702062:0.440928:0.702062:0.429327:0.685575:0.429327:0.000000:0.000000:0.000000
 :@0.702062:0.441192:0.705097:0.441192:0.705097:0.429388:0.702062:0.429388:0.000000
λ:@0.675618:0.441375:0.683055:0.441375:0.683055:0.429927:0.675618:0.429927:0.000000
λ:@0.758230:0.505015:0.765668:0.505015:0.765668:0.493566:0.758230:0.493566:0.000000
p:@0.787313:0.563001:0.798794:0.563001:0.798794:0.552976:0.787313:0.552976:0.000000
 Figura 3.22.:@0.798794:0.563708:0.856154:0.563708:0.856154:0.552232:0.798794:0.552232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.684804:0.596860:0.752269:0.596860:0.752269:0.579177:0.684804:0.579177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
absurdo. :@0.685042:0.623673:0.745305:0.623673:0.745305:0.608412:0.685042:0.608412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Contrario y :@0.745129:0.623475:0.820696:0.623475:0.820696:0.608412:0.745129:0.608412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
opuesto a la razón, que no tiene :@0.638498:0.639317:0.844525:0.639317:0.844525:0.624254:0.638498:0.624254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sentido.:@0.638498:0.655159:0.688067:0.655159:0.688067:0.640096:0.638498:0.640096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.632070:0.600591:0.643474:0.599082:0.638272:0.576937:0.626867:0.578446:0.000000
c:@0.635451:0.611561:0.646050:0.610158:0.640968:0.588523:0.630369:0.589926:0.000000
b:@0.645827:0.604343:0.658540:0.602660:0.653408:0.580818:0.640695:0.582500:0.000000
Competencia :@0.684804:0.688250:0.782426:0.688250:0.782426:0.672777:0.684804:0.672777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684804:0.700818:0.768866:0.700818:0.768866:0.685345:0.684804:0.685345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Puesto que :@0.685042:0.730083:0.761189:0.730083:0.761189:0.715020:0.685042:0.715020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.785950:0.731039:0.796526:0.731039:0.796526:0.714759:0.785950:0.714759:0.000000
u:@0.772502:0.730519:0.781711:0.730519:0.781711:0.714050:0.772502:0.714050:0.000000
0:@0.764180:0.730403:0.772676:0.730403:0.772676:0.713906:0.764180:0.713906:0.000000
0:@0.800610:0.730403:0.809106:0.730403:0.809106:0.713906:0.800610:0.713906:0.000000
, el :@0.813120:0.730083:0.833877:0.730083:0.833877:0.715020:0.813120:0.715020:0.000000:0.000000:0.000000:0.000000:0.000000
vector nulo es colineal a todo :@0.638504:0.745925:0.834614:0.745925:0.834614:0.730862:0.638504:0.730862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vector de  .:@0.638504:0.761767:0.723797:0.761767:0.723797:0.746704:0.638504:0.746704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.704062:0.760882:0.716762:0.760882:0.716762:0.748605:0.704062:0.748605:0.000000
2:@0.716761:0.755967:0.721283:0.755967:0.721283:0.747186:0.716761:0.747186:0.000000
Dos vectores no nulos de    :@0.638503:0.784737:0.831886:0.784736:0.831886:0.769673:0.638503:0.769674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.807105:0.783853:0.819805:0.783853:0.819805:0.771575:0.807105:0.771575:0.000000
2:@0.819799:0.778937:0.824322:0.778937:0.824322:0.770155:0.819799:0.770155:0.000000
se dicen linealmente indepen-:@0.638502:0.800578:0.833292:0.800578:0.833292:0.785515:0.638502:0.785515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dientes si no son colineales.:@0.638502:0.816420:0.816141:0.816420:0.816141:0.801357:0.638502:0.801357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vectores colineales se dicen :@0.638502:0.839391:0.845112:0.839391:0.845112:0.824328:0.638502:0.824328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
también linealmente depen-:@0.638502:0.855233:0.823230:0.855233:0.823230:0.840170:0.638502:0.840170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dientes.:@0.638502:0.871075:0.688051:0.871075:0.688051:0.856012:0.638502:0.856012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tres vectores no nulos de   :@0.638502:0.894046:0.828104:0.894045:0.828104:0.878982:0.638502:0.878983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.807101:0.893161:0.819801:0.893161:0.819801:0.880884:0.807101:0.880884:0.000000
2:@0.819801:0.888244:0.824324:0.888244:0.824324:0.879462:0.819801:0.879462:0.000000
son linealmente dependientes. :@0.638502:0.909887:0.840206:0.909887:0.840206:0.894824:0.638502:0.894824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Investiga por qué.:@0.638502:0.925729:0.752941:0.925729:0.752941:0.910666:0.638502:0.910666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000