19:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000 En el caso de un sistema :@0.685308:0.130778:0.846026:0.130778:0.846026:0.115714:0.685308:0.115714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ecuaciones lineales :@0.638501:0.146620:0.784954:0.146620:0.784954:0.131556:0.638501:0.131556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diagonal:@0.784954:0.146818:0.842455:0.146818:0.842455:0.131556:0.784954:0.131556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.842457:0.146620:0.848754:0.146620:0.848754:0.131556:0.842457:0.131556:0.000000:0.000000 la solución es única si y solo si :@0.638501:0.162462:0.835824:0.162462:0.835824:0.147398:0.638501:0.147398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los coeficientes de la diagonal :@0.638501:0.178304:0.834116:0.178304:0.834116:0.163240:0.638501:0.163240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del sistema son no nulos, es :@0.638501:0.194146:0.821101:0.194146:0.821101:0.179082:0.638501:0.179082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decir, ≠ 0, ≠ 0, ≠ 0. En :@0.638501:0.209987:0.827439:0.209987:0.827439:0.194924:0.638501:0.194924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.676126:0.210093:0.684323:0.210093:0.684323:0.195056:0.676126:0.195056:0.000000 1:@0.684325:0.212981:0.688847:0.212981:0.688847:0.204199:0.684325:0.204199:0.000000 b:@0.720334:0.210093:0.728795:0.210093:0.728795:0.195056:0.720334:0.195056:0.000000 2:@0.728794:0.212981:0.733316:0.212981:0.733316:0.204199:0.728794:0.204199:0.000000 c:@0.764801:0.210093:0.771362:0.210093:0.771362:0.195056:0.764801:0.195056:0.000000 3:@0.771362:0.212981:0.775884:0.212981:0.775884:0.204199:0.771362:0.204199:0.000000 este caso, la solución es::@0.638505:0.225829:0.792819:0.225829:0.792819:0.210766:0.638505:0.210766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.638505:0.254345:0.645330:0.254345:0.645330:0.239308:0.638505:0.239308:0.000000 = , = , = ,:@0.645330:0.254239:0.801459:0.254239:0.801459:0.239176:0.645330:0.239176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.695532:0.254345:0.702550:0.254345:0.702550:0.239308:0.695532:0.239308:0.000000 z:@0.752752:0.254345:0.758821:0.254345:0.758821:0.239308:0.752752:0.239308:0.000000 que expresamos como: :@0.638505:0.285923:0.795936:0.285923:0.795936:0.270860:0.638505:0.270860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , , .:@0.704767:0.314333:0.780386:0.314333:0.780386:0.299270:0.704767:0.299270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los sistemas de ecuaciones :@0.638505:0.342334:0.817235:0.342334:0.817235:0.327271:0.638505:0.327271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lineales triangulares superiores :@0.638505:0.358176:0.837730:0.358176:0.837730:0.343113:0.638505:0.343113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e inferiores tienen una única so-:@0.638505:0.374018:0.844940:0.374018:0.844940:0.358955:0.638505:0.358955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lución si y solo si los elementos :@0.638505:0.389860:0.843322:0.389860:0.843322:0.374797:0.638505:0.374797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la diagonal del sistema son :@0.638505:0.405702:0.834034:0.405702:0.834034:0.390639:0.638505:0.390639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 no nulos, esto es::@0.638505:0.421544:0.748685:0.421544:0.748685:0.406481:0.638505:0.406481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.678857:0.437492:0.687053:0.437492:0.687053:0.422455:0.678857:0.422455:0.000000 1:@0.687047:0.440387:0.691569:0.440387:0.691569:0.431606:0.687047:0.431606:0.000000 ≠ 0, ≠ 0, ≠ 0.:@0.691568:0.437396:0.806310:0.437396:0.806310:0.422332:0.691568:0.422332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.723054:0.437501:0.731515:0.437501:0.731515:0.422464:0.723054:0.422464:0.000000 2:@0.731514:0.440387:0.736037:0.440387:0.736037:0.431606:0.731514:0.431606:0.000000 c:@0.767524:0.437501:0.774085:0.437501:0.774085:0.422464:0.767524:0.422464:0.000000 3:@0.774084:0.440387:0.778606:0.440387:0.778606:0.431606:0.774084:0.431606:0.000000 La idea fundamental en el :@0.638501:0.460776:0.813502:0.460776:0.813502:0.445713:0.638501:0.445713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 método de eliminación gaussia-:@0.638501:0.476618:0.844987:0.476618:0.844987:0.461555:0.638501:0.461555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 na es transformar el sistema de :@0.638501:0.492460:0.841224:0.492460:0.841224:0.477397:0.638501:0.477397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuaciones lineales dado en un :@0.638501:0.508302:0.843509:0.508302:0.843509:0.493239:0.638501:0.493239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sistema de ecuaciones lineales :@0.638501:0.524144:0.836631:0.524144:0.836631:0.509081:0.638501:0.509081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 triangular superior que, como :@0.638501:0.539986:0.834452:0.539986:0.834452:0.524923:0.638501:0.524923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hemos visto, es el más simple :@0.638501:0.555828:0.830932:0.555828:0.830932:0.540765:0.638501:0.540765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de resolver.:@0.638501:0.571670:0.710407:0.571670:0.710407:0.556607:0.638501:0.556607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.668358:0.247136:0.676731:0.247136:0.676731:0.232099:0.668358:0.232099:0.000000 1:@0.676731:0.248766:0.681253:0.248766:0.681253:0.239984:0.676731:0.239984:0.000000 a:@0.668445:0.262223:0.676642:0.262223:0.676642:0.247187:0.668445:0.247187:0.000000 1:@0.676642:0.265111:0.681164:0.265111:0.681164:0.256329:0.676642:0.256329:0.000000 d:@0.685110:0.307486:0.693483:0.307486:0.693483:0.292449:0.685110:0.292449:0.000000 1:@0.693483:0.309116:0.698006:0.309116:0.698006:0.300335:0.693483:0.300335:0.000000 a:@0.685197:0.322574:0.693394:0.322574:0.693394:0.307537:0.685197:0.307537:0.000000 1:@0.693394:0.325461:0.697917:0.325461:0.697917:0.316679:0.693394:0.316679:0.000000 d:@0.723641:0.247136:0.732014:0.247136:0.732014:0.232099:0.723641:0.232099:0.000000 2:@0.732014:0.248766:0.736536:0.248766:0.736536:0.239984:0.732014:0.239984:0.000000 b:@0.723597:0.262223:0.732058:0.262223:0.732058:0.247187:0.723597:0.247187:0.000000 2:@0.732057:0.265111:0.736580:0.265111:0.736580:0.256329:0.732057:0.256329:0.000000 d:@0.716940:0.307486:0.725313:0.307486:0.725313:0.292449:0.716940:0.292449:0.000000 2:@0.725313:0.309116:0.729835:0.309116:0.729835:0.300335:0.725313:0.300335:0.000000 b:@0.716896:0.322574:0.725357:0.322574:0.725357:0.307537:0.716896:0.307537:0.000000 2:@0.725356:0.325461:0.729879:0.325461:0.729879:0.316679:0.725356:0.316679:0.000000 d:@0.778924:0.247136:0.787296:0.247136:0.787296:0.232099:0.778924:0.232099:0.000000 3:@0.787296:0.248766:0.791819:0.248766:0.791819:0.239984:0.787296:0.239984:0.000000 c:@0.779830:0.262223:0.786391:0.262223:0.786391:0.247187:0.779830:0.247187:0.000000 3:@0.786390:0.265111:0.790913:0.265111:0.790913:0.256329:0.786390:0.256329:0.000000 d:@0.752120:0.307486:0.760493:0.307486:0.760493:0.292449:0.752120:0.292449:0.000000 3:@0.760493:0.309116:0.765015:0.309116:0.765015:0.300335:0.760493:0.300335:0.000000 c:@0.753026:0.322574:0.759587:0.322574:0.759587:0.307537:0.753026:0.307537:0.000000 3:@0.759586:0.325461:0.764109:0.325461:0.764109:0.316679:0.759586:0.316679:0.000000 Ejercicio resuelto:@0.108233:0.096570:0.226211:0.096570:0.226211:0.079783:0.108233:0.079783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideremos el siguiente sistema de ecuaciones lineales,:@0.108233:0.113545:0.513067:0.113545:0.513067:0.097047:0.108233:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde ( , , ) :@0.108233:0.130896:0.210397:0.130896:0.210397:0.114398:0.108233:0.114398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.165162:0.131011:0.200417:0.131011:0.200417:0.114543:0.165162:0.114543:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.210339:0.130679:0.226387:0.130679:0.226387:0.116032:0.210339:0.116032:0.000000 :@0.226326:0.130377:0.230723:0.130377:0.230723:0.117004:0.226326:0.117004:0.000000 :@0.230671:0.129927:0.244581:0.129927:0.244581:0.116480:0.230671:0.116480:0.000000 3:@0.244522:0.124544:0.249475:0.124544:0.249475:0.114926:0.244522:0.114926:0.000000 son las incógnitas::@0.249442:0.130896:0.381754:0.130896:0.381754:0.114398:0.249442:0.114398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + = –2,:@0.288686:0.155375:0.416780:0.155375:0.416780:0.138877:0.288686:0.138877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.307874:0.155490:0.319491:0.155490:0.319491:0.139022:0.307874:0.139022:0.000000:0.000000 y:@0.342725:0.155490:0.350412:0.155490:0.350412:0.139022:0.342725:0.139022:0.000000 3 + 4 + = –2,:@0.288686:0.172725:0.417204:0.172725:0.417204:0.156228:0.288686:0.156228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.307874:0.172841:0.319491:0.172841:0.319491:0.156372:0.307874:0.156372:0.000000:0.000000 y z:@0.342937:0.172841:0.376362:0.172841:0.376362:0.156372:0.342937:0.156372:0.000000:0.000000:0.000000:0.000000 –3 + 4 + = 4.:@0.288686:0.190076:0.406512:0.190076:0.406512:0.173579:0.288686:0.173579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.307681:0.190192:0.319298:0.190192:0.319298:0.173723:0.307681:0.173723:0.000000:0.000000 y z:@0.342744:0.190192:0.376169:0.190192:0.376169:0.173723:0.342744:0.173723:0.000000:0.000000:0.000000:0.000000 Aplicamos el método de eliminación gaussiana. Mantenemos fija :@0.108228:0.224778:0.599854:0.224778:0.599854:0.208280:0.108228:0.208280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a la primera ecuación y eliminamos la incógnita de la incógni-:@0.108228:0.242129:0.595691:0.242129:0.595691:0.225631:0.108228:0.225631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.477501:0.242244:0.484976:0.242244:0.484976:0.225775:0.477501:0.225775:0.000000 ta en la segunda y tercera ecuaciones. Multiplicamos a la primera :@0.108228:0.259479:0.599949:0.259479:0.599949:0.242982:0.108228:0.242982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.127956:0.259595:0.135431:0.259595:0.135431:0.243126:0.127956:0.243126:0.000000 ecuación por = – ; sumamos el resultado a la segunda ecuación:@0.108228:0.283958:0.591356:0.283958:0.591356:0.267461:0.108228:0.267461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.206132:0.284074:0.214378:0.284074:0.214378:0.267605:0.206132:0.267605:0.000000 y obtenemos: :@0.108228:0.308437:0.216921:0.308437:0.216921:0.291940:0.108228:0.291940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + = –2,:@0.288686:0.332916:0.416780:0.332916:0.416780:0.316419:0.288686:0.316419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.307874:0.333032:0.319491:0.333032:0.319491:0.316563:0.307874:0.316563:0.000000:0.000000 y:@0.342725:0.333032:0.350412:0.333032:0.350412:0.316563:0.342725:0.316563:0.000000 + = 1,:@0.288686:0.357395:0.406300:0.357395:0.406300:0.340898:0.288686:0.340898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.342532:0.357511:0.375957:0.357511:0.375957:0.341042:0.342532:0.341042:0.000000:0.000000:0.000000:0.000000 –3 + 4 + = 4.:@0.288686:0.381874:0.406512:0.381874:0.406512:0.365377:0.288686:0.365377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.307681:0.381990:0.319298:0.381990:0.319298:0.365521:0.307681:0.365521:0.000000:0.000000 y z:@0.342744:0.381990:0.376169:0.381990:0.376169:0.365521:0.342744:0.365521:0.000000:0.000000:0.000000:0.000000 Sea = – = .:@0.108228:0.416576:0.250836:0.416575:0.250836:0.400077:0.108228:0.400078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.136490:0.416692:0.144736:0.416692:0.144736:0.400223:0.136490:0.400223:0.000000 1:@0.144740:0.419853:0.149693:0.419853:0.149693:0.410234:0.144740:0.410234:0.000000 Multiplicamos la primera ecuación por y sumamos el resultado a :@0.108235:0.441054:0.599896:0.441054:0.599896:0.424557:0.108235:0.424556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.393990:0.441169:0.402236:0.441169:0.402236:0.424701:0.393990:0.424701:0.000000 1:@0.402253:0.444331:0.407206:0.444331:0.407206:0.434713:0.402253:0.434713:0.000000 la tercera ecuación::@0.108227:0.458405:0.243891:0.458405:0.243891:0.441907:0.108227:0.441907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + = –2,:@0.288685:0.482884:0.409651:0.482884:0.409651:0.466386:0.288685:0.466386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.300745:0.483000:0.312362:0.483000:0.312362:0.466531:0.300745:0.466531:0.000000:0.000000 y:@0.335596:0.483000:0.343283:0.483000:0.343283:0.466531:0.335596:0.466531:0.000000 + = 1,:@0.288685:0.507363:0.402157:0.507363:0.402157:0.490865:0.288685:0.490865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.338389:0.507479:0.371814:0.507479:0.371814:0.491010:0.338389:0.491010:0.000000:0.000000:0.000000:0.000000 + = 1.:@0.288685:0.538970:0.402157:0.538970:0.402157:0.522473:0.288685:0.522473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.338389:0.539086:0.371814:0.539086:0.371814:0.522617:0.338389:0.522617:0.000000:0.000000:0.000000:0.000000 Para obtener un sistema de ecuaciones triangular superior, mantene-:@0.108227:0.573672:0.595736:0.573672:0.595736:0.557174:0.108227:0.557174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mos fijas la primera y segunda ecuaciones del sistema precedente; :@0.108227:0.591023:0.599905:0.591023:0.599905:0.574525:0.108227:0.574525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 eliminamos la incógnita de la tercera ecuación.:@0.108227:0.608373:0.450567:0.608373:0.450567:0.591876:0.108227:0.591876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.281227:0.608489:0.288914:0.608489:0.288914:0.592020:0.281227:0.592020:0.000000 Sea = – = – ( se obtiene dividiendo el coeficiente de de :@0.108227:0.651866:0.599963:0.651871:0.599963:0.635373:0.108227:0.635368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.136451:0.651982:0.144696:0.651982:0.144696:0.635513:0.136451:0.635513:0.000000 2:@0.144695:0.655148:0.149648:0.655148:0.149648:0.645530:0.144695:0.645530:0.000000 k:@0.272079:0.651987:0.280325:0.651987:0.280325:0.635518:0.272079:0.635518:0.000000 2:@0.280201:0.655148:0.285155:0.655148:0.285155:0.645530:0.280201:0.645530:0.000000 y:@0.566172:0.651987:0.573859:0.651987:0.573859:0.635518:0.566172:0.635518:0.000000 la tercera ecuación para el coeficiente de de la segunda ecuación, :@0.108242:0.693701:0.599886:0.693701:0.599886:0.677203:0.108242:0.677203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.409950:0.693816:0.417637:0.693816:0.417637:0.677348:0.409950:0.677348:0.000000 cambiado de signo). Multiplicamos a la segunda ecuación por y :@0.108242:0.711051:0.599912:0.711051:0.599912:0.694553:0.108242:0.694554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.568851:0.711167:0.577097:0.711167:0.577097:0.694698:0.568851:0.694698:0.000000 2:@0.577062:0.714328:0.582015:0.714328:0.582015:0.704709:0.577062:0.704709:0.000000 sumamos el resultado a la tercera::@0.108224:0.728402:0.347284:0.728402:0.347284:0.711904:0.108224:0.711904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + = –2,:@0.288681:0.752881:0.412056:0.752881:0.412056:0.736383:0.288681:0.736383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.303150:0.752996:0.314767:0.752996:0.314767:0.736528:0.303150:0.736528:0.000000:0.000000 y:@0.338001:0.752996:0.345687:0.752996:0.345687:0.736528:0.338001:0.736528:0.000000 + = 1,:@0.288681:0.777360:0.402154:0.777360:0.402154:0.760862:0.288681:0.760862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.338386:0.777475:0.371811:0.777475:0.371811:0.761007:0.338386:0.761007:0.000000:0.000000:0.000000:0.000000 :@0.288681:0.808967:0.334244:0.808967:0.334244:0.792469:0.288681:0.792469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – z:@0.334244:0.809083:0.371638:0.809083:0.371638:0.792614:0.334244:0.792614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = – ,:@0.371638:0.808967:0.424694:0.808967:0.424694:0.792469:0.371638:0.792469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con lo que obtenemos un sistema de ecuaciones triangular superior. Así, :@0.108224:0.843668:0.599962:0.843668:0.599962:0.827171:0.108224:0.827171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 determinamos su solución. De la tercera ecuación obtenemos::@0.108224:0.861019:0.535964:0.861019:0.535964:0.844522:0.108224:0.844522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.219635:0.885614:0.226281:0.885614:0.226281:0.869145:0.219635:0.869145:0.000000 = 1, = (1 – ) = (1 – 1) = 0.:@0.226281:0.885498:0.484339:0.885498:0.484339:0.869001:0.226281:0.869001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.273192:0.885614:0.280879:0.885614:0.280879:0.869145:0.273192:0.869145:0.000000 z:@0.353914:0.885614:0.360560:0.885614:0.360560:0.869145:0.353914:0.869145:0.000000 De la primera ecuación se deduce : = (–2 – ) = (–2 – 0) = –1.:@0.108224:0.920200:0.595635:0.920200:0.595635:0.903702:0.108224:0.903702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.347477:0.920315:0.369307:0.920315:0.369307:0.903847:0.347477:0.903847:0.000000:0.000000:0.000000 y:@0.448082:0.920315:0.455769:0.920315:0.455769:0.903847:0.448082:0.903847:0.000000 La solución del sistema de ecuaciones lineales propuesto es (–1, 0, 1).:@0.108224:0.953398:0.595822:0.953398:0.595822:0.936900:0.108224:0.936900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.251949:0.276382:0.260444:0.276382:0.260444:0.259884:0.251949:0.259884:0.000000 2:@0.251949:0.292720:0.260444:0.292720:0.260444:0.276223:0.251949:0.276223:0.000000 5:@0.325837:0.349827:0.334333:0.349827:0.334333:0.333329:0.325837:0.333329:0.000000 2:@0.325837:0.366166:0.334333:0.366166:0.334333:0.349668:0.325837:0.349668:0.000000 5:@0.322486:0.501502:0.330982:0.501502:0.330982:0.485004:0.322486:0.485004:0.000000 2:@0.322486:0.517840:0.330982:0.517840:0.330982:0.501342:0.322486:0.501342:0.000000 11:@0.314093:0.531347:0.331278:0.531347:0.331278:0.514850:0.314093:0.514850:0.000000:0.000000 2:@0.318428:0.547686:0.326924:0.547686:0.326924:0.531188:0.318428:0.531188:0.000000 –3:@0.186686:0.409016:0.205874:0.409016:0.205874:0.392518:0.186686:0.392518:0.000000:0.000000 2:@0.192042:0.425354:0.200538:0.425354:0.200538:0.408857:0.192042:0.408857:0.000000 3:@0.234189:0.409016:0.242685:0.409016:0.242685:0.392518:0.234189:0.392518:0.000000 2:@0.234189:0.425354:0.242685:0.425354:0.242685:0.408857:0.234189:0.408857:0.000000 11:@0.240597:0.644487:0.257782:0.644487:0.257782:0.627989:0.240597:0.627989:0.000000:0.000000 5:@0.244932:0.660825:0.253428:0.660825:0.253428:0.644328:0.244932:0.644328:0.000000 11:@0.186579:0.627291:0.203764:0.627291:0.203764:0.610793:0.186579:0.610793:0.000000:0.000000 2:@0.190914:0.643629:0.199410:0.643629:0.199410:0.627132:0.190914:0.627132:0.000000 5:@0.190925:0.661238:0.199421:0.661238:0.199421:0.644740:0.190925:0.644740:0.000000 2:@0.190925:0.677576:0.199421:0.677576:0.199421:0.661079:0.190925:0.661079:0.000000 5:@0.321236:0.769613:0.329732:0.769613:0.329732:0.753116:0.321236:0.753116:0.000000 2:@0.321236:0.785952:0.329732:0.785952:0.329732:0.769454:0.321236:0.769454:0.000000 6:@0.349253:0.801340:0.357749:0.801340:0.357749:0.784842:0.349253:0.784842:0.000000 5:@0.349253:0.817679:0.357749:0.817679:0.357749:0.801181:0.349253:0.801181:0.000000 6:@0.406422:0.801340:0.414918:0.801340:0.414918:0.784842:0.406422:0.784842:0.000000 5:@0.406422:0.817679:0.414918:0.817679:0.414918:0.801181:0.406422:0.801181:0.000000 1:@0.390779:0.912371:0.399275:0.912371:0.399275:0.895873:0.390779:0.895873:0.000000 2:@0.390779:0.928710:0.399275:0.928710:0.399275:0.912212:0.390779:0.912212:0.000000 2:@0.303904:0.877612:0.312400:0.877612:0.312400:0.861114:0.303904:0.861114:0.000000 5:@0.303904:0.893950:0.312400:0.893950:0.312400:0.877453:0.303904:0.877453:0.000000 2:@0.389342:0.877612:0.397838:0.877612:0.397838:0.861114:0.389342:0.861114:0.000000 5:@0.389342:0.893950:0.397838:0.893950:0.397838:0.877453:0.389342:0.877453:0.000000 1:@0.483353:0.912371:0.491849:0.912371:0.491849:0.895873:0.483353:0.895873:0.000000 2:@0.483353:0.928710:0.491849:0.928710:0.491849:0.912212:0.483353:0.912212:0.000000 Glosario:@0.684804:0.620416:0.752269:0.620416:0.752269:0.602734:0.684804:0.602734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diagonal. :@0.685042:0.647230:0.749333:0.647230:0.749333:0.631969:0.685042:0.631969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dicho de una :@0.749333:0.647032:0.841135:0.647032:0.841135:0.631969:0.749333:0.631969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 línea recta que une dos vértices :@0.638498:0.662874:0.846391:0.662874:0.846391:0.647811:0.638498:0.647811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 no contiguos de un polígono o :@0.638498:0.678716:0.843860:0.678716:0.843860:0.663652:0.638498:0.663652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de distinta cara en un poliedro.:@0.638498:0.694558:0.839742:0.694558:0.839742:0.679494:0.638498:0.679494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.632070:0.624148:0.643474:0.622639:0.638272:0.600494:0.626867:0.602003:0.000000 c:@0.635451:0.635117:0.646050:0.633715:0.640968:0.612080:0.630369:0.613483:0.000000 b:@0.645827:0.627900:0.658540:0.626217:0.653408:0.604375:0.640695:0.606057:0.000000 Competencia :@0.685072:0.096006:0.782695:0.096006:0.782695:0.080533:0.685072:0.080533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.685072:0.108574:0.769134:0.108574:0.769134:0.093101:0.685072:0.093101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Historia:@0.684773:0.767041:0.840336:0.767041:0.840336:0.751569:0.684773:0.751569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La eliminación de Gauss-Jordan :@0.638230:0.786025:0.846493:0.786025:0.846493:0.770962:0.638230:0.770962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se llama así en honor de Carl :@0.638230:0.801867:0.828027:0.801867:0.828027:0.786804:0.638230:0.786804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Friedrich Gauss (matemático, :@0.638230:0.817709:0.831314:0.817709:0.831314:0.802646:0.638230:0.802646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 astrónomo y físico alemán :@0.638230:0.833551:0.812528:0.833551:0.812528:0.818488:0.638230:0.818488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que contribuyó en la teoría de :@0.638230:0.849393:0.837699:0.849393:0.837699:0.834330:0.638230:0.834330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números, el análisis matemático, :@0.638230:0.865235:0.849664:0.865235:0.849664:0.850172:0.638230:0.850172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la geometría diferencial, la esta-:@0.638230:0.881077:0.839829:0.881077:0.839829:0.866014:0.638230:0.866014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dística y el álgebra) y Wilhelm :@0.638230:0.896919:0.834586:0.896919:0.834586:0.881856:0.638230:0.881856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Jordan (geodesista alemán que :@0.638230:0.912761:0.840811:0.912761:0.840811:0.897698:0.638230:0.897698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 creó un algoritmo para la elimi-:@0.638230:0.928603:0.841675:0.928603:0.841675:0.913540:0.638230:0.913540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 nación de ecuaciones lineales).:@0.638230:0.944445:0.836748:0.944445:0.836748:0.929382:0.638230:0.929382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad:@0.684537:0.737991:0.831322:0.737991:0.831322:0.722519:0.684537:0.722519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@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