18:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000 Método de eliminación gaussiana:@0.404235:0.120539:0.811820:0.120539:0.811820:0.075879:0.404235:0.075879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.1.10. Resolver sistemas de ecuaciones lineales con tres incógnitas (infinitas soluciones), utilizando los métodos de sustitución o eliminación gaussiana.:@0.143847:0.949804:0.805164:0.949804:0.805164:0.939761:0.143847:0.939761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consta de tres etapas. Las dos primeras conducen a transformar el :@0.404236:0.146090:0.895843:0.146090:0.895843:0.129593:0.404236:0.129593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sistema de ecuaciones en uno triangular superior; y la tercera etapa :@0.404236:0.163441:0.895918:0.163441:0.895918:0.146943:0.404236:0.146943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 consiste en resolver el sistema de ecuaciones triangular superior.:@0.404236:0.180792:0.855500:0.180792:0.855500:0.164294:0.404236:0.164294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.404236:0.215869:0.522215:0.215869:0.522215:0.199082:0.404236:0.199082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resolvamos el siguiente sistema :@0.404236:0.232844:0.632162:0.232844:0.632162:0.216346:0.404236:0.216346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ecuaciones lineales: :@0.404236:0.250195:0.567679:0.250195:0.567679:0.233697:0.404236:0.233697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , , ) :@0.404236:0.267545:0.455366:0.267545:0.455366:0.251048:0.404236:0.251048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.410131:0.267661:0.445387:0.267661:0.445387:0.251192:0.410131:0.251192:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.455308:0.267329:0.471356:0.267329:0.471356:0.252682:0.455308:0.252682:0.000000 :@0.471296:0.267027:0.475694:0.267027:0.475694:0.253654:0.471296:0.253654:0.000000 :@0.475642:0.266577:0.489551:0.266577:0.489551:0.253130:0.475642:0.253130:0.000000 3:@0.489492:0.261194:0.494446:0.261194:0.494446:0.251576:0.489492:0.251576:0.000000 Primera etapa:@0.404236:0.302710:0.512985:0.302710:0.512985:0.285764:0.404236:0.285764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Mantenemos fija la primera ecuación. Se trata de eli-:@0.512985:0.302247:0.891830:0.302247:0.891830:0.285749:0.512985:0.285749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 minar la incógnita de la segunda y tercera ecuaciones. :@0.404236:0.319598:0.800654:0.319598:0.800654:0.303100:0.404236:0.303100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.536762:0.319713:0.544237:0.319713:0.544237:0.303245:0.536762:0.303245:0.000000 Eliminemos de la segunda ecuación. Para el efecto, multiplicamos por :@0.404236:0.354299:0.895901:0.354299:0.895901:0.337802:0.404236:0.337802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.488811:0.354415:0.496286:0.354415:0.496286:0.337946:0.488811:0.337946:0.000000 k:@0.404236:0.371766:0.412482:0.371766:0.412482:0.355297:0.404236:0.355297:0.000000 = –2 (coeficiente de de la segunda ecuación, dividido para el coe-:@0.412289:0.371650:0.891799:0.371650:0.891799:0.355152:0.412289:0.355152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.564770:0.371766:0.572245:0.371766:0.572245:0.355297:0.564770:0.355297:0.000000 ficiente de de la primera ecuación cambiado de signo) a la primera :@0.404236:0.389001:0.895864:0.389001:0.895864:0.372503:0.404236:0.372503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.483070:0.389116:0.490545:0.389116:0.490545:0.372648:0.483070:0.372648:0.000000 ecuación y le sumamos el resultado a la segunda ecuación. Obtenemos: :@0.404236:0.406352:0.895912:0.406352:0.895912:0.389854:0.404236:0.389854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + 2 + 3 = 7,:@0.584694:0.430831:0.700305:0.430831:0.700305:0.414333:0.584694:0.414333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.592978:0.430946:0.604595:0.430946:0.604595:0.414477:0.592978:0.414477:0.000000:0.000000 y:@0.628041:0.430946:0.635728:0.430946:0.635728:0.414477:0.628041:0.414477:0.000000 z:@0.663315:0.430946:0.669962:0.430946:0.669962:0.414477:0.663315:0.414477:0.000000 :@0.584694:0.448297:0.603574:0.448297:0.603574:0.431828:0.584694:0.431828:0.000000:0.000000:0.000000:0.000000 – 5 – 8 = –14,:@0.604344:0.448181:0.718433:0.448181:0.718433:0.431684:0.604344:0.431684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.627482:0.448297:0.635169:0.448297:0.635169:0.431828:0.627482:0.431828:0.000000 z:@0.662448:0.448297:0.669095:0.448297:0.669095:0.431828:0.662448:0.431828:0.000000 3 – 2 + 5 = 25.:@0.584694:0.465532:0.708704:0.465532:0.708704:0.449034:0.584694:0.449034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.593190:0.465648:0.604807:0.465648:0.604807:0.449179:0.593190:0.449179:0.000000:0.000000 y:@0.627944:0.465648:0.635631:0.465648:0.635631:0.449179:0.627944:0.449179:0.000000 z:@0.663219:0.465648:0.669866:0.465648:0.669866:0.449179:0.663219:0.449179:0.000000 Eliminemos de la tercera ecuación. Para ello, multiplicamos por :@0.404236:0.490011:0.895843:0.490011:0.895843:0.473513:0.404236:0.473513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.494552:0.490127:0.502027:0.490127:0.502027:0.473658:0.494552:0.473658:0.000000 k:@0.404236:0.507477:0.412482:0.507477:0.412482:0.491009:0.404236:0.491009:0.000000 = –3 (coeficiente de de la tercera ecuación, dividido para el coe-:@0.412482:0.507362:0.891855:0.507362:0.891855:0.490864:0.412482:0.490864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.568239:0.507477:0.575714:0.507477:0.575714:0.491009:0.568239:0.491009:0.000000 ficiente de de la primera ecuación cambiado de signo) a la primera :@0.404236:0.524713:0.895866:0.524713:0.895866:0.508215:0.404236:0.508215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.483070:0.524828:0.490545:0.524828:0.490545:0.508359:0.483070:0.508359:0.000000 ecuación, y le sumamos el resultado a la tercera ecuación. Se obtiene: :@0.404236:0.542063:0.895845:0.542063:0.895845:0.525566:0.404236:0.525566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + 2 + 3 = 7,:@0.584694:0.566542:0.700305:0.566542:0.700305:0.550045:0.584694:0.550045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.592978:0.566658:0.604595:0.566658:0.604595:0.550189:0.592978:0.550189:0.000000:0.000000 y:@0.628041:0.566658:0.635728:0.566658:0.635728:0.550189:0.628041:0.550189:0.000000 z:@0.663315:0.566658:0.669962:0.566658:0.669962:0.550189:0.663315:0.550189:0.000000 :@0.584694:0.584009:0.603574:0.584009:0.603574:0.567540:0.584694:0.567540:0.000000:0.000000:0.000000:0.000000 – 5 – 8 = –14,:@0.604344:0.583893:0.718433:0.583893:0.718433:0.567395:0.604344:0.567395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.627482:0.584009:0.635169:0.584009:0.635169:0.567540:0.627482:0.567540:0.000000 z:@0.662448:0.584009:0.669095:0.584009:0.669095:0.567540:0.662448:0.567540:0.000000 :@0.584694:0.601360:0.603574:0.601360:0.603574:0.584891:0.584694:0.584891:0.000000:0.000000:0.000000:0.000000 – 8 – 4 = 4.:@0.604344:0.601244:0.699438:0.601244:0.699438:0.584746:0.604344:0.584746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.627482:0.601360:0.635169:0.601360:0.635169:0.584891:0.627482:0.584891:0.000000 z:@0.662448:0.601360:0.669095:0.601360:0.669095:0.584891:0.662448:0.584891:0.000000 Segunda etapa:@0.404236:0.626186:0.517901:0.626186:0.517901:0.609240:0.404236:0.609240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Mantenemos fijas la primera y segunda ecuaciones,:@0.517901:0.625723:0.891815:0.625723:0.891815:0.609225:0.517901:0.609225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y eliminamos en la tercera ecuación. Multiplicamos por – = –:@0.404236:0.650202:0.872305:0.650202:0.872305:0.633704:0.404236:0.633704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.501314:0.650318:0.509001:0.650318:0.509001:0.633849:0.501314:0.633849:0.000000 a la segunda ecuación, y el resultado se suma a la tercera. Obtenemos :@0.404236:0.674681:0.895911:0.674681:0.895911:0.658183:0.404236:0.658183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.489716:0.699276:0.501333:0.699276:0.501333:0.682807:0.489716:0.682807:0.000000:0.000000 + 2 + 3 = 7,:@0.501333:0.699160:0.597043:0.699160:0.597043:0.682662:0.501333:0.682662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.524779:0.699276:0.532466:0.699276:0.532466:0.682807:0.524779:0.682807:0.000000 z:@0.560054:0.699276:0.566700:0.699276:0.566700:0.682807:0.560054:0.682807:0.000000 :@0.489716:0.716626:0.502528:0.716626:0.502528:0.700158:0.489716:0.700158:0.000000:0.000000:0.000000 – 5 – 8 = –14,:@0.502720:0.716511:0.616809:0.716511:0.616809:0.700013:0.502720:0.700013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.525858:0.716626:0.533545:0.716626:0.533545:0.700158:0.525858:0.700158:0.000000 z:@0.560824:0.716626:0.567471:0.716626:0.567471:0.700158:0.560824:0.700158:0.000000 z:@0.489716:0.739327:0.567837:0.739327:0.567837:0.722858:0.489716:0.722858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = .:@0.567837:0.739211:0.618678:0.739211:0.618678:0.722714:0.567837:0.722714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tercera etapa:@0.404236:0.776226:0.504720:0.776226:0.504720:0.759280:0.404236:0.759280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Resolvemos el sistema de ecuaciones triangular superior.:@0.504454:0.775764:0.891776:0.775764:0.891776:0.759266:0.504454:0.759266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Comenzamos con la tercera ecuación. Obtenemos : = = 3.:@0.404236:0.800243:0.866136:0.800243:0.866136:0.783745:0.404236:0.783745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z z:@0.767517:0.800358:0.787707:0.800358:0.787707:0.783889:0.767517:0.783889:0.000000:0.000000:0.000000 De la segunda ecuación obtenemos ::@0.404236:0.832428:0.672886:0.832428:0.672886:0.815931:0.404236:0.815931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.662445:0.832544:0.670131:0.832544:0.670131:0.816075:0.662445:0.816075:0.000000 y:@0.404236:0.857023:0.411923:0.857023:0.411923:0.840554:0.404236:0.840554:0.000000 = = = –2,:@0.411923:0.856907:0.623494:0.856907:0.623494:0.840410:0.411923:0.840410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y de la primera ecuación obtenemos: :@0.404236:0.881386:0.670767:0.881386:0.670767:0.864889:0.404236:0.864889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.404236:0.898853:0.411711:0.898853:0.411711:0.882384:0.404236:0.882384:0.000000 = 7 – 2 – 3 = 7 – 2 (–2) – 3 × 3 = 2.:@0.411711:0.898737:0.686646:0.898737:0.686646:0.882239:0.411711:0.882239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.466579:0.898853:0.474265:0.898853:0.474265:0.882384:0.466579:0.882384:0.000000 z:@0.501545:0.898853:0.508192:0.898853:0.508192:0.882384:0.501545:0.882384:0.000000 x:@0.563059:0.898853:0.570534:0.898853:0.570534:0.882384:0.563059:0.882384:0.000000 La solución es = 2, = –2, = 3, que se escribe (2, –2, 3).:@0.404236:0.923216:0.811827:0.923216:0.811827:0.906718:0.404236:0.906718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.507708:0.923332:0.515183:0.923332:0.515183:0.906863:0.507708:0.906863:0.000000 y:@0.549668:0.923332:0.557354:0.923332:0.557354:0.906863:0.549668:0.906863:0.000000 z:@0.602339:0.923332:0.608985:0.923332:0.608985:0.906863:0.602339:0.906863:0.000000 Saberes previos:@0.199646:0.101454:0.307805:0.101454:0.307805:0.085981:0.199646:0.085981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué es un sistema lineal :@0.199884:0.130082:0.365019:0.130082:0.365019:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ecuaciones diagonales?:@0.153341:0.145924:0.322432:0.145924:0.322432:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desequilibrio cognitivo:@0.199646:0.193076:0.363493:0.193076:0.363493:0.177603:0.199646:0.177603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En un sistema de ecua-:@0.199884:0.221703:0.348590:0.221703:0.348590:0.206640:0.199884:0.206640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciones lineales diagonal, ¿qué :@0.153341:0.237545:0.344085:0.237545:0.344085:0.222482:0.153341:0.222482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 condiciones deben cumplir los :@0.153341:0.253387:0.356467:0.253387:0.356467:0.238324:0.153341:0.238324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 coeficientes de la diagonal para :@0.153341:0.269229:0.359476:0.269229:0.359476:0.254166:0.153341:0.254166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que la solución del sistema sea :@0.153341:0.285071:0.354444:0.285071:0.354444:0.270008:0.153341:0.270008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 única?:@0.153341:0.300913:0.194149:0.300913:0.194149:0.285850:0.153341:0.285850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –8:@0.821971:0.642117:0.841159:0.642117:0.841159:0.625619:0.821971:0.625619:0.000000:0.000000 –5:@0.821971:0.658455:0.841159:0.658455:0.841159:0.641958:0.821971:0.641958:0.000000:0.000000 8:@0.880398:0.642117:0.888894:0.642117:0.888894:0.625619:0.880398:0.625619:0.000000 5:@0.880398:0.658455:0.888894:0.658455:0.888894:0.641958:0.880398:0.641958:0.000000 44:@0.539304:0.734017:0.556489:0.734017:0.556489:0.717519:0.539304:0.717519:0.000000:0.000000 5:@0.543639:0.750355:0.552135:0.750355:0.552135:0.733858:0.543639:0.733858:0.000000 132:@0.587946:0.734017:0.613820:0.734017:0.613820:0.717519:0.587946:0.717519:0.000000:0.000000:0.000000 5:@0.596635:0.750355:0.605131:0.750355:0.605131:0.733858:0.596635:0.733858:0.000000 132:@0.808920:0.792958:0.834794:0.792958:0.834794:0.776460:0.808920:0.776460:0.000000:0.000000:0.000000 44:@0.813274:0.809296:0.830459:0.809296:0.830459:0.792799:0.813274:0.792799:0.000000:0.000000 14 – 8z:@0.433372:0.852120:0.484714:0.852120:0.484714:0.835622:0.433372:0.835622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.454795:0.868459:0.463291:0.868459:0.463291:0.851961:0.454795:0.851961:0.000000 14 – 8 × 3:@0.508947:0.852120:0.576953:0.852120:0.576953:0.835622:0.508947:0.835622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.538693:0.868459:0.547189:0.868459:0.547189:0.851961:0.538693:0.851961:0.000000 Este es un sistema de ecuaciones :@0.658754:0.734279:0.895059:0.734279:0.895059:0.717782:0.658754:0.717782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 triangular :@0.658754:0.751630:0.730786:0.751630:0.730786:0.735133:0.658754:0.735133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 superior:@0.730786:0.752093:0.795402:0.752093:0.795402:0.735147:0.730786:0.735147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.795402:0.751630:0.798157:0.751630:0.798157:0.735133:0.795402:0.735133:0.000000 + 2 + 3 = 7,:@0.685783:0.232640:0.801394:0.232640:0.801394:0.216143:0.685783:0.216143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.694067:0.232756:0.705684:0.232756:0.705684:0.216287:0.694067:0.216287:0.000000:0.000000 y:@0.729130:0.232756:0.736816:0.232756:0.736816:0.216287:0.729130:0.216287:0.000000 z:@0.764404:0.232756:0.771051:0.232756:0.771051:0.216287:0.764404:0.216287:0.000000 2 – – 2 = 0,:@0.685783:0.249991:0.800777:0.249991:0.800777:0.233493:0.685783:0.233493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.694279:0.250107:0.705896:0.250107:0.705896:0.233638:0.694279:0.233638:0.000000:0.000000 y:@0.728821:0.250107:0.736508:0.250107:0.736508:0.233638:0.728821:0.233638:0.000000 z:@0.763788:0.250107:0.770434:0.250107:0.770434:0.233638:0.763788:0.233638:0.000000 3 – 2 + 5 = 25.:@0.685783:0.267342:0.809793:0.267342:0.809793:0.250844:0.685783:0.250844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.694279:0.267457:0.705896:0.267457:0.705896:0.250989:0.694279:0.250989:0.000000:0.000000 y:@0.729033:0.267457:0.736720:0.267457:0.736720:0.250989:0.729033:0.250989:0.000000 z:@0.764308:0.267457:0.770955:0.267457:0.770955:0.250989:0.764308:0.250989:0.000000 Los sistemas de tres :@0.200418:0.472971:0.330794:0.472971:0.330794:0.457908:0.200418:0.457908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuaciones con tres incógnitas :@0.153347:0.488813:0.355242:0.488813:0.355242:0.473750:0.153347:0.473750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 más simples de resolver son :@0.153347:0.504655:0.337265:0.504655:0.337265:0.489592:0.153347:0.489592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sistemas diagonales:@0.153347:0.520695:0.284655:0.520695:0.284655:0.505434:0.153347:0.505434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x:@0.177094:0.536444:0.207978:0.536444:0.207978:0.521408:0.177094:0.521408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.196632:0.539331:0.201155:0.539331:0.201155:0.530549:0.196632:0.530549:0.000000 = ,:@0.286307:0.536339:0.316088:0.536339:0.316088:0.521276:0.286307:0.521276:0.000000:0.000000:0.000000 d:@0.299957:0.536444:0.308330:0.536444:0.308330:0.521408:0.299957:0.521408:0.000000 1:@0.308332:0.539331:0.312855:0.539331:0.312855:0.530549:0.308332:0.530549:0.000000 :@0.177091:0.552181:0.226255:0.552181:0.226255:0.537118:0.177091:0.537118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b y:@0.226255:0.552286:0.246254:0.552286:0.246254:0.537250:0.226255:0.537250:0.000000:0.000000:0.000000 2:@0.234714:0.555173:0.239236:0.555173:0.239236:0.546391:0.234714:0.546391:0.000000 = , ,:@0.286306:0.552181:0.345076:0.552181:0.345076:0.537118:0.286306:0.537118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.299956:0.552286:0.308329:0.552286:0.308329:0.537250:0.299956:0.537250:0.000000 2:@0.308332:0.555173:0.312855:0.555173:0.312855:0.546391:0.308332:0.546391:0.000000 = .:@0.177091:0.568023:0.316088:0.568023:0.316088:0.552960:0.177091:0.552960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c z d:@0.267856:0.568128:0.308328:0.568128:0.308328:0.553092:0.267856:0.553092:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.274413:0.571015:0.278936:0.571015:0.278936:0.562233:0.274413:0.562233:0.000000 3:@0.308332:0.571015:0.312855:0.571015:0.312855:0.562233:0.308332:0.562233:0.000000 los :@0.153345:0.590994:0.175121:0.590994:0.175121:0.575931:0.153345:0.575931:0.000000:0.000000:0.000000:0.000000 triangulares superiores:@0.175121:0.591192:0.327572:0.591192:0.327572:0.575931:0.175121:0.575931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.327574:0.590994:0.331356:0.590994:0.331356:0.575931:0.327574:0.575931:0.000000 a x b y + c z d:@0.190899:0.606941:0.308332:0.606940:0.308332:0.591903:0.190899:0.591905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.199095:0.609826:0.203617:0.609826:0.203617:0.601044:0.199095:0.601044:0.000000 + :@0.210443:0.606834:0.227874:0.606834:0.227874:0.591771:0.210443:0.591771:0.000000:0.000000:0.000000 1:@0.236334:0.609826:0.240856:0.609826:0.240856:0.601044:0.236334:0.601044:0.000000 1:@0.271937:0.609826:0.276460:0.609826:0.276460:0.601044:0.271937:0.601044:0.000000 = ,:@0.282528:0.606834:0.316140:0.606834:0.316140:0.591771:0.282528:0.591771:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.308332:0.609826:0.312855:0.609826:0.312855:0.601044:0.308332:0.601044:0.000000 :@0.153344:0.622676:0.228365:0.622676:0.228365:0.607613:0.153344:0.607613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b y + c z d:@0.228541:0.622782:0.309000:0.622782:0.309000:0.607745:0.228541:0.607745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.237002:0.625668:0.241525:0.625668:0.241525:0.616886:0.237002:0.616886:0.000000 2:@0.272606:0.625668:0.277128:0.625668:0.277128:0.616886:0.272606:0.616886:0.000000 = , ,:@0.283196:0.622676:0.345796:0.622676:0.345796:0.607613:0.283196:0.607613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.309000:0.625668:0.313523:0.625668:0.313523:0.616886:0.309000:0.616886:0.000000 :@0.153344:0.638518:0.157126:0.638518:0.157126:0.623455:0.153344:0.623455:0.000000 c:@0.264988:0.638624:0.271549:0.638624:0.271549:0.623587:0.264988:0.623587:0.000000 3:@0.271550:0.641510:0.276073:0.641510:0.276073:0.632728:0.271550:0.632728:0.000000 z = . :@0.276072:0.638518:0.319921:0.638518:0.319921:0.623455:0.276072:0.623455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.299959:0.638624:0.308332:0.638624:0.308332:0.623587:0.299959:0.623587:0.000000 3:@0.308332:0.641510:0.312855:0.641510:0.312855:0.632728:0.308332:0.632728:0.000000 y los :@0.153344:0.661489:0.186044:0.661489:0.186044:0.646426:0.153344:0.646426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 triangulares inferiores:@0.186044:0.661687:0.331671:0.661687:0.331671:0.646426:0.186044:0.646426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x:@0.186589:0.677437:0.206131:0.677436:0.206131:0.662399:0.186589:0.662400:0.000000:0.000000:0.000000 1:@0.194784:0.680323:0.199307:0.680323:0.199307:0.671541:0.194784:0.671541:0.000000 = ,:@0.206131:0.677330:0.313303:0.677330:0.313303:0.662267:0.206131:0.662267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.297177:0.677436:0.305549:0.677436:0.305549:0.662399:0.297177:0.662399:0.000000 1:@0.305548:0.680323:0.310070:0.680323:0.310070:0.671541:0.305548:0.671541:0.000000 a x b y d:@0.186585:0.693278:0.305251:0.693278:0.305251:0.678241:0.186585:0.678241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.194784:0.696165:0.199307:0.696165:0.199307:0.687383:0.194784:0.687383:0.000000 + :@0.206131:0.693172:0.223562:0.693172:0.223562:0.678109:0.206131:0.678109:0.000000:0.000000:0.000000 2:@0.232023:0.696165:0.236546:0.696165:0.236546:0.687383:0.232023:0.687383:0.000000 = , ,:@0.283229:0.693172:0.342045:0.693172:0.342045:0.678109:0.283229:0.678109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.305250:0.696165:0.309772:0.696165:0.309772:0.687383:0.305250:0.687383:0.000000 a x b y + c z d:@0.186585:0.709120:0.304022:0.709120:0.304022:0.694083:0.186585:0.694083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.194784:0.712007:0.199307:0.712007:0.199307:0.703225:0.194784:0.703225:0.000000 + :@0.206131:0.709014:0.223562:0.709014:0.223562:0.693951:0.206131:0.693951:0.000000:0.000000:0.000000 3:@0.232023:0.712007:0.236546:0.712007:0.236546:0.703225:0.232023:0.703225:0.000000 3:@0.267625:0.712007:0.272148:0.712007:0.272148:0.703225:0.267625:0.703225:0.000000 = .:@0.278217:0.709014:0.311571:0.709014:0.311571:0.693951:0.278217:0.693951:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.304020:0.712007:0.308542:0.712007:0.308542:0.703225:0.304020:0.703225:0.000000 donde , , :@0.153349:0.735549:0.246233:0.735548:0.246233:0.720485:0.153349:0.720486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.199945:0.735655:0.240643:0.735654:0.240643:0.720617:0.199945:0.720618:0.000000:0.000000:0.000000:0.000000:0.000000 i:@0.208032:0.738603:0.210052:0.738603:0.210052:0.729836:0.208032:0.729836:0.000000 i:@0.225252:0.738603:0.227272:0.738603:0.227272:0.729836:0.225252:0.729836:0.000000 i:@0.240431:0.738603:0.242451:0.738603:0.242451:0.729836:0.240431:0.729836:0.000000 :@0.246234:0.735199:0.260189:0.735199:0.260189:0.722463:0.246234:0.722463:0.000000 :@0.260189:0.735350:0.264587:0.735350:0.264587:0.721977:0.260189:0.721977:0.000000 :@0.264587:0.734664:0.277287:0.734664:0.277287:0.722386:0.264587:0.722386:0.000000 para :@0.277287:0.735548:0.313364:0.735548:0.313364:0.720485:0.277287:0.720485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i:@0.153347:0.751496:0.156812:0.751496:0.156812:0.736459:0.153347:0.736459:0.000000 = 1, 2, 3, no todos nulos, :@0.156812:0.751390:0.321350:0.751390:0.321350:0.736327:0.156812:0.736327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d:@0.153347:0.767338:0.161720:0.767338:0.161720:0.752301:0.153347:0.752301:0.000000 i:@0.161613:0.770287:0.163633:0.770287:0.163633:0.761520:0.161613:0.761520:0.000000 :@0.163633:0.767232:0.167415:0.767232:0.167415:0.752169:0.163633:0.752169:0.000000 :@0.167416:0.766883:0.181371:0.766883:0.181371:0.754147:0.167416:0.754147:0.000000 :@0.181369:0.767034:0.185766:0.767034:0.185766:0.753661:0.181369:0.753661:0.000000 :@0.185766:0.766348:0.198466:0.766348:0.198466:0.754070:0.185766:0.754070:0.000000 para = 1, 2, 3, donde :@0.198466:0.767232:0.344198:0.767232:0.344198:0.752169:0.198466:0.752169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i:@0.234544:0.767338:0.238009:0.767338:0.238009:0.752301:0.234544:0.752301:0.000000 ( , , ) :@0.153346:0.784903:0.204996:0.784903:0.204996:0.768406:0.153346:0.768406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.159299:0.785019:0.194901:0.785019:0.194901:0.768550:0.159299:0.768550:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.204995:0.784385:0.224045:0.784385:0.224045:0.771012:0.204995:0.771012:0.000000:0.000000 :@0.224044:0.783935:0.237954:0.783935:0.237954:0.770488:0.224044:0.770488:0.000000 3:@0.237954:0.778552:0.242907:0.778552:0.242907:0.768934:0.237954:0.768934:0.000000 son las incógnitas :@0.242906:0.784583:0.364715:0.784583:0.364715:0.769520:0.242906:0.769520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del sistema que queremos :@0.153337:0.800425:0.325385:0.800425:0.325385:0.785362:0.153337:0.785362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 obtener. A los números reales :@0.153337:0.816267:0.347793:0.816267:0.347793:0.801204:0.153337:0.801204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.153337:0.832214:0.197752:0.832214:0.197752:0.817178:0.153337:0.817178:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.161543:0.835163:0.165839:0.835163:0.165839:0.826397:0.161543:0.826397:0.000000 , , que figuran en la diago-:@0.165840:0.832109:0.358510:0.832109:0.358510:0.817046:0.165840:0.817046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.180597:0.835163:0.184894:0.835163:0.184894:0.826397:0.180597:0.826397:0.000000 3:@0.197751:0.835163:0.202048:0.835163:0.202048:0.826397:0.197751:0.826397:0.000000 nal de cada uno de los sistemas :@0.153341:0.847951:0.360374:0.847951:0.360374:0.832888:0.153341:0.832888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 precedentes se los denomina :@0.153341:0.863793:0.345739:0.863793:0.345739:0.848730:0.153341:0.848730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elementos o coeficientes de la :@0.153341:0.879635:0.352123:0.879635:0.352123:0.864572:0.153341:0.864572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diagonal del sistema de ecua-:@0.153341:0.895477:0.342749:0.895477:0.342749:0.880414:0.153341:0.880414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciones lineales.:@0.153341:0.911319:0.248150:0.911319:0.248150:0.896256:0.153341:0.896256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.200180:0.436450:0.297803:0.436450:0.297803:0.420978:0.200180:0.420978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.200180:0.449018:0.284243:0.449018:0.284243:0.433546:0.200180:0.433546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000