18:@0.058599:0.966558:0.074760:0.966558:0.074760:0.950778:0.058599:0.950778:0.000000:0.000000 M.5.1.15. Realizar las operaciones de potencias de matrices M [R], aplicando las propiedades de números reales.:@0.148948:0.939096:0.637700:0.939096:0.637700:0.929054:0.148948:0.929054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2×2:@0.412772:0.941091:0.422637:0.941091:0.422637:0.935237:0.412772:0.935237:0.000000:0.000000:0.000000 M.5.1.16. Calcular el producto de una matriz de M [R] por un vector en el plano, y analizar su resultado (vector y no matriz).:@0.148948:0.947897:0.692559:0.947897:0.692559:0.937855:0.148948:0.937855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2×2:@0.365044:0.949892:0.374909:0.949892:0.374909:0.944038:0.365044:0.944038:0.000000:0.000000:0.000000 Matrices especiales:@0.404235:0.120964:0.634463:0.120964:0.634463:0.076304:0.404235:0.076304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matriz invertible e inversa:@0.404236:0.147650:0.613481:0.147650:0.613481:0.129967:0.404236:0.129967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición :@0.404236:0.164820:0.491103:0.164820:0.491103:0.147874:0.404236:0.147874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea :@0.484322:0.164358:0.553570:0.164358:0.553570:0.147860:0.484322:0.147860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.519365:0.164473:0.530636:0.164473:0.530636:0.148004:0.519365:0.148004:0.000000 :@0.534774:0.163839:0.549427:0.163839:0.549427:0.150466:0.534774:0.150466:0.000000 M:@0.553570:0.164473:0.568847:0.164473:0.568847:0.148004:0.553570:0.148004:0.000000 2×2:@0.568847:0.167635:0.585054:0.167635:0.585054:0.158017:0.568847:0.158017:0.000000:0.000000:0.000000 [ ].:@0.585053:0.164358:0.612826:0.164358:0.612826:0.147860:0.585053:0.147860:0.000000:0.000000:0.000000:0.000000 R:@0.590910:0.163271:0.604215:0.163271:0.604215:0.150408:0.590910:0.150408:0.000000 i):@0.404241:0.199276:0.414779:0.199276:0.414779:0.182561:0.404241:0.182561:0.000000:0.000000 Se dice que la matriz es invertible si y solo si existe una matriz :@0.414779:0.199059:0.880378:0.199059:0.880378:0.182561:0.414779:0.182561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.577821:0.199175:0.589091:0.199175:0.589091:0.182706:0.577821:0.182706:0.000000 B:@0.427976:0.216525:0.437166:0.216525:0.437166:0.200057:0.427976:0.200057:0.000000 :@0.437166:0.216410:0.460105:0.216410:0.460105:0.199912:0.437166:0.199912:0.000000:0.000000:0.000000 :@0.441311:0.215891:0.455963:0.215891:0.455963:0.202518:0.441311:0.202518:0.000000 M:@0.460105:0.216525:0.475382:0.216525:0.475382:0.200057:0.460105:0.200057:0.000000 2×2:@0.475382:0.219688:0.491589:0.219688:0.491589:0.210070:0.475382:0.210070:0.000000:0.000000:0.000000 [ ] tal que :@0.491590:0.216410:0.574034:0.216410:0.574034:0.199912:0.491590:0.199912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.497447:0.215323:0.510751:0.215323:0.510751:0.202461:0.497447:0.202461:0.000000 AB BA:@0.574034:0.216525:0.634144:0.216525:0.634144:0.200057:0.574034:0.200057:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.594380:0.216410:0.613472:0.216410:0.613472:0.199912:0.594380:0.199912:0.000000:0.000000:0.000000 = .:@0.634144:0.216410:0.660991:0.216410:0.660991:0.199912:0.634144:0.199912:0.000000:0.000000:0.000000:0.000000:0.000000 ӏ:@0.653234:0.223996:0.658228:0.223996:0.658228:0.204997:0.653234:0.204997:0.000000 ii):@0.404243:0.251328:0.419039:0.251328:0.419039:0.234614:0.404243:0.234614:0.000000:0.000000:0.000000 Se dice que es singular si y solo si no es invertible, y que es :@0.419039:0.251111:0.895775:0.251111:0.895775:0.234614:0.419039:0.234614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.514498:0.251227:0.525768:0.251227:0.525768:0.234758:0.514498:0.234758:0.000000 A:@0.684666:0.251227:0.695936:0.251227:0.695936:0.234758:0.684666:0.234758:0.000000 A:@0.861386:0.251227:0.872656:0.251227:0.872656:0.234758:0.861386:0.234758:0.000000 no singular si y solo si es invertible.:@0.427978:0.268462:0.687671:0.268462:0.687671:0.251964:0.427978:0.251964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.584334:0.268578:0.595605:0.268578:0.595605:0.252109:0.584334:0.252109:0.000000 :@0.404243:0.285813:0.408385:0.285813:0.408385:0.269315:0.404243:0.269315:0.000000 Si A es invertible su inversa se nota :@0.427978:0.285813:0.673155:0.285813:0.673155:0.269315:0.427978:0.269315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.672384:0.285928:0.683655:0.285928:0.683655:0.269460:0.672384:0.269460:0.000000 –1:@0.683619:0.279461:0.694694:0.279461:0.694694:0.269843:0.683619:0.269843:0.000000:0.000000 , es decir que, = :@0.694693:0.285813:0.818143:0.285813:0.818143:0.269315:0.694693:0.269315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B A:@0.790641:0.285928:0.828642:0.285928:0.828642:0.269460:0.790641:0.269460:0.000000:0.000000:0.000000 –1:@0.828611:0.279461:0.839686:0.279461:0.839686:0.269843:0.828611:0.269843:0.000000:0.000000 . Luego, :@0.839686:0.285813:0.895920:0.285813:0.895920:0.269315:0.839686:0.269315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AA:@0.427988:0.303279:0.450528:0.303279:0.450528:0.286810:0.427988:0.286810:0.000000:0.000000 –1:@0.450520:0.296812:0.461594:0.296812:0.461594:0.287194:0.450520:0.287194:0.000000:0.000000 = :@0.461593:0.303164:0.480685:0.303164:0.480685:0.286666:0.461593:0.286666:0.000000:0.000000:0.000000 A A:@0.480685:0.303279:0.514300:0.303279:0.514300:0.286810:0.480685:0.286810:0.000000:0.000000:0.000000 –1:@0.491955:0.296812:0.503029:0.296812:0.503029:0.287194:0.491955:0.287194:0.000000:0.000000 = .:@0.514300:0.303164:0.541149:0.303164:0.541149:0.286666:0.514300:0.286666:0.000000:0.000000:0.000000:0.000000:0.000000 ӏ:@0.533390:0.310750:0.538384:0.310750:0.538384:0.291751:0.533390:0.291751:0.000000 :@0.404231:0.320514:0.408373:0.320514:0.408373:0.304017:0.404231:0.304017:0.000000 A la matriz :@0.427966:0.320514:0.508687:0.320514:0.508687:0.304017:0.427966:0.304017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.508687:0.320630:0.519958:0.320630:0.519958:0.304161:0.508687:0.304161:0.000000 –1:@0.519972:0.314163:0.531046:0.314163:0.531046:0.304544:0.519972:0.304544:0.000000:0.000000 se le llama matriz inversa de .:@0.531045:0.320514:0.750515:0.320514:0.750515:0.304017:0.531045:0.304017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.736490:0.320630:0.747760:0.320630:0.747760:0.304161:0.736490:0.304161:0.000000 Ejercicio resuelto:@0.404241:0.355592:0.522220:0.355592:0.522220:0.338805:0.404241:0.338805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean = , = Si: :@0.404241:0.386144:0.683682:0.386144:0.683682:0.369646:0.404241:0.369646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.442040:0.386259:0.453310:0.386259:0.453310:0.369790:0.442040:0.369790:0.000000 B:@0.545571:0.386259:0.554761:0.386259:0.554761:0.369790:0.545571:0.369790:0.000000 AB BA = B = A:@0.683682:0.386259:0.834049:0.386261:0.834049:0.369792:0.683682:0.369790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.704028:0.386144:0.723120:0.386144:0.723120:0.369646:0.704028:0.369646:0.000000:0.000000:0.000000 ӏ:@0.762949:0.393732:0.767942:0.393732:0.767942:0.374733:0.762949:0.374733:0.000000 ⇒:@0.772094:0.385501:0.790282:0.385501:0.790282:0.368559:0.772094:0.368559:0.000000 –1:@0.834047:0.379794:0.845122:0.379794:0.845122:0.370176:0.834047:0.370176:0.000000:0.000000 .:@0.845122:0.386145:0.847877:0.386145:0.847877:0.369648:0.845122:0.369648:0.000000 AB:@0.404237:0.438313:0.424581:0.438313:0.424581:0.421845:0.404237:0.421845:0.000000:0.000000 = , :@0.424581:0.438198:0.568760:0.438198:0.568760:0.421700:0.424581:0.421700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB:@0.568760:0.438313:0.589105:0.438313:0.589105:0.421845:0.568760:0.421845:0.000000:0.000000 = . Por lo tanto, = :@0.589106:0.438198:0.788694:0.438198:0.788694:0.421700:0.589106:0.421700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B A:@0.760413:0.438313:0.799965:0.438313:0.799965:0.421845:0.760413:0.421845:0.000000:0.000000:0.000000 –1:@0.799958:0.431846:0.811032:0.431846:0.811032:0.422228:0.799958:0.422228:0.000000:0.000000 = .:@0.811031:0.438198:0.886724:0.438198:0.886724:0.421700:0.811031:0.421700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Potencia de matrices:@0.404236:0.491647:0.571068:0.491647:0.571068:0.473965:0.404236:0.473965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.404236:0.508818:0.484320:0.508818:0.484320:0.491872:0.404236:0.491872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea :@0.484322:0.508355:0.553685:0.508355:0.553685:0.491857:0.484322:0.491857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.519481:0.508471:0.530751:0.508471:0.530751:0.492002:0.519481:0.492002:0.000000 :@0.534890:0.507836:0.549542:0.507836:0.549542:0.494463:0.534890:0.494463:0.000000 M:@0.553685:0.508471:0.568962:0.508471:0.568962:0.492002:0.553685:0.492002:0.000000 2×2:@0.568962:0.511633:0.585170:0.511633:0.585170:0.502015:0.568962:0.502015:0.000000:0.000000:0.000000 [ ] con ≠ 0.:@0.585169:0.508355:0.687036:0.508355:0.687036:0.491857:0.585169:0.491857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.591025:0.507268:0.604330:0.507268:0.604330:0.494406:0.591025:0.494406:0.000000 A:@0.645423:0.508471:0.656693:0.508471:0.656693:0.492002:0.645423:0.492002:0.000000 i):@0.404241:0.543273:0.414779:0.543273:0.414779:0.526559:0.404241:0.526559:0.000000:0.000000 Se define :@0.414779:0.543057:0.497291:0.543057:0.497291:0.526559:0.414779:0.526559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.497291:0.543172:0.508561:0.543172:0.508561:0.526704:0.497291:0.526704:0.000000 m:@0.508565:0.536705:0.517247:0.536705:0.517247:0.527087:0.508565:0.527087:0.000000 recursivamente como sigue: = , :@0.517246:0.543057:0.774354:0.543057:0.774354:0.526559:0.517246:0.526559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.722997:0.543172:0.734267:0.543172:0.734267:0.526704:0.722997:0.526704:0.000000 0:@0.734267:0.536705:0.739220:0.536705:0.739220:0.527087:0.734267:0.527087:0.000000 ӏ:@0.758311:0.550643:0.763305:0.550643:0.763305:0.531644:0.758311:0.531644:0.000000 A:@0.774354:0.543172:0.785625:0.543172:0.785625:0.526704:0.774354:0.526704:0.000000 m:@0.785546:0.536772:0.794172:0.536772:0.794172:0.527171:0.785546:0.527171:0.000000 +1:@0.794172:0.536705:0.805426:0.536705:0.805426:0.527087:0.794172:0.527087:0.000000:0.000000 = :@0.805426:0.543057:0.824518:0.543057:0.824518:0.526559:0.805426:0.526559:0.000000:0.000000:0.000000 A A, :@0.824518:0.543172:0.862985:0.543172:0.862985:0.526704:0.824518:0.526704:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.835711:0.536772:0.844337:0.536772:0.844337:0.527171:0.835711:0.527171:0.000000 :@0.404241:0.560407:0.408383:0.560407:0.408383:0.543910:0.404241:0.543910:0.000000 m:@0.427976:0.560523:0.442772:0.560523:0.442772:0.544054:0.427976:0.544054:0.000000 = 0, 1, … .:@0.442772:0.560407:0.514593:0.560407:0.514593:0.543910:0.442772:0.543910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ii):@0.404241:0.595326:0.419037:0.595326:0.419037:0.578611:0.404241:0.578611:0.000000:0.000000:0.000000 Si es invertible, se define :@0.419037:0.595109:0.618950:0.595109:0.618950:0.578611:0.419037:0.578611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.443928:0.595225:0.455198:0.595225:0.455198:0.578756:0.443928:0.578756:0.000000 A:@0.618950:0.595225:0.630221:0.595225:0.630221:0.578756:0.618950:0.578756:0.000000 –:@0.630221:0.588757:0.636342:0.588757:0.636342:0.579139:0.630221:0.579139:0.000000 m:@0.636342:0.588825:0.644968:0.588825:0.644968:0.579223:0.636342:0.579223:0.000000 = (:@0.644968:0.595109:0.670013:0.595109:0.670013:0.578611:0.644968:0.578611:0.000000:0.000000:0.000000:0.000000 A:@0.670013:0.595225:0.681283:0.595225:0.681283:0.578756:0.670013:0.578756:0.000000 –1:@0.681282:0.588757:0.692357:0.588757:0.692357:0.579139:0.681282:0.579139:0.000000:0.000000 ) , = 0, 1, … .:@0.692357:0.595109:0.800449:0.595109:0.800449:0.578611:0.692357:0.578611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.698309:0.588825:0.706935:0.588825:0.706935:0.579223:0.698309:0.579223:0.000000 m:@0.713832:0.595225:0.728628:0.595225:0.728628:0.578756:0.713832:0.578756:0.000000 :@0.404240:0.612460:0.408382:0.612460:0.408382:0.595962:0.404240:0.595962:0.000000 De la definición: :@0.427974:0.612460:0.546704:0.612460:0.546704:0.595962:0.427974:0.595962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404240:0.629810:0.408382:0.629810:0.408382:0.613313:0.404240:0.613313:0.000000 A:@0.427974:0.629926:0.439245:0.629926:0.439245:0.613457:0.427974:0.613457:0.000000 1:@0.439250:0.623459:0.444204:0.623459:0.444204:0.613840:0.439250:0.613840:0.000000 = :@0.444202:0.629810:0.463294:0.629810:0.463294:0.613313:0.444202:0.613313:0.000000:0.000000:0.000000 A:@0.463294:0.629926:0.474564:0.629926:0.474564:0.613457:0.463294:0.613457:0.000000 0+1:@0.474564:0.623459:0.490772:0.623459:0.490772:0.613840:0.474564:0.613840:0.000000:0.000000:0.000000 = :@0.490771:0.629810:0.509863:0.629810:0.509863:0.613313:0.490771:0.613313:0.000000:0.000000:0.000000 A A = A = A, :@0.509863:0.629926:0.610388:0.629926:0.610388:0.613457:0.509863:0.613457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.521133:0.623459:0.526086:0.623459:0.526086:0.613840:0.521133:0.613840:0.000000 ӏ:@0.556524:0.636884:0.561291:0.636884:0.561291:0.618749:0.556524:0.618749:0.000000 A:@0.641675:0.629926:0.652945:0.629926:0.652945:0.613457:0.641675:0.613457:0.000000 2:@0.652942:0.623459:0.657895:0.623459:0.657895:0.613840:0.652942:0.613840:0.000000 = :@0.657894:0.629810:0.676986:0.629810:0.676986:0.613313:0.657894:0.613313:0.000000:0.000000:0.000000 A:@0.676986:0.629926:0.688256:0.629926:0.688256:0.613457:0.676986:0.613457:0.000000 1+1:@0.688256:0.623459:0.704464:0.623459:0.704464:0.613840:0.688256:0.613840:0.000000:0.000000:0.000000 = :@0.704463:0.629810:0.723554:0.629810:0.723554:0.613313:0.704463:0.613313:0.000000:0.000000:0.000000 A A = AA,:@0.723554:0.629926:0.795992:0.629926:0.795992:0.613457:0.723554:0.613457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.734825:0.623459:0.739778:0.623459:0.739778:0.613840:0.734825:0.613840:0.000000 :@0.404235:0.647161:0.408377:0.647161:0.408377:0.630663:0.404235:0.630663:0.000000 A:@0.427970:0.647277:0.439240:0.647277:0.439240:0.630808:0.427970:0.630808:0.000000 3:@0.439250:0.640809:0.444204:0.640809:0.444204:0.631191:0.439250:0.631191:0.000000 = :@0.444202:0.647161:0.463294:0.647161:0.463294:0.630663:0.444202:0.630663:0.000000:0.000000:0.000000 A:@0.463294:0.647277:0.474564:0.647277:0.474564:0.630808:0.463294:0.630808:0.000000 2+1:@0.474564:0.640809:0.490772:0.640809:0.490772:0.631191:0.474564:0.631191:0.000000:0.000000:0.000000 = :@0.490771:0.647161:0.509863:0.647161:0.509863:0.630663:0.490771:0.630663:0.000000:0.000000:0.000000 A A = AAA, :@0.509863:0.647277:0.597713:0.647277:0.597713:0.630808:0.509863:0.630808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.521133:0.640809:0.526086:0.640809:0.526086:0.631191:0.521133:0.631191:0.000000 A:@0.641678:0.647277:0.652948:0.647277:0.652948:0.630808:0.641678:0.630808:0.000000 4:@0.652942:0.640809:0.657895:0.640809:0.657895:0.631191:0.652942:0.631191:0.000000 = :@0.657894:0.647161:0.676986:0.647161:0.676986:0.630663:0.657894:0.630663:0.000000:0.000000:0.000000 A:@0.676986:0.647277:0.688256:0.647277:0.688256:0.630808:0.676986:0.630808:0.000000 3+1:@0.688256:0.640809:0.704464:0.640809:0.704464:0.631191:0.688256:0.631191:0.000000:0.000000:0.000000 = :@0.704463:0.647161:0.723554:0.647161:0.723554:0.630663:0.704463:0.630663:0.000000:0.000000:0.000000 A A = AAAA, :@0.723554:0.647277:0.822675:0.647277:0.822675:0.630808:0.723554:0.630808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.734825:0.640809:0.739778:0.640809:0.739778:0.631191:0.734825:0.631191:0.000000 :@0.404235:0.664512:0.408377:0.664512:0.408377:0.648014:0.404235:0.648014:0.000000 y así sucesivamente.:@0.427970:0.664512:0.568836:0.664512:0.568836:0.648014:0.427970:0.648014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si es invertible, :@0.427970:0.699213:0.551401:0.699213:0.551401:0.682716:0.427970:0.682716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.443922:0.699329:0.455192:0.699329:0.455192:0.682860:0.443922:0.682860:0.000000 A:@0.551401:0.699329:0.562671:0.699329:0.562671:0.682860:0.551401:0.682860:0.000000 –1:@0.562679:0.692862:0.573753:0.692862:0.573753:0.683244:0.562679:0.683244:0.000000:0.000000 = (:@0.573754:0.699213:0.598799:0.699213:0.598799:0.682716:0.573754:0.682716:0.000000:0.000000:0.000000:0.000000 A:@0.598799:0.699329:0.610069:0.699329:0.610069:0.682860:0.598799:0.682860:0.000000 –1 1:@0.610068:0.692862:0.632048:0.692862:0.632048:0.683244:0.610068:0.683244:0.000000:0.000000:0.000000:0.000000 ):@0.621141:0.699213:0.627094:0.699213:0.627094:0.682716:0.621141:0.682716:0.000000 , A:@0.632047:0.699329:0.652950:0.699329:0.652950:0.682860:0.632047:0.682860:0.000000:0.000000:0.000000 –2:@0.652942:0.692862:0.664017:0.692862:0.664017:0.683244:0.652942:0.683244:0.000000:0.000000 = (:@0.664016:0.699213:0.689060:0.699213:0.689060:0.682716:0.664016:0.682716:0.000000:0.000000:0.000000:0.000000 A:@0.689060:0.699329:0.700331:0.699329:0.700331:0.682860:0.689060:0.682860:0.000000 –1 2:@0.700330:0.692862:0.722310:0.692862:0.722310:0.683244:0.700330:0.683244:0.000000:0.000000:0.000000:0.000000 ) = :@0.711405:0.699213:0.741402:0.699213:0.741402:0.682716:0.711405:0.682716:0.000000:0.000000:0.000000:0.000000:0.000000 A A ,:@0.741402:0.699329:0.790064:0.699329:0.790064:0.682860:0.741402:0.682860:0.000000:0.000000:0.000000:0.000000:0.000000 –1:@0.752673:0.692862:0.763747:0.692862:0.763747:0.683244:0.752673:0.683244:0.000000:0.000000 –1:@0.775015:0.692862:0.786090:0.692862:0.786090:0.683244:0.775015:0.683244:0.000000:0.000000 A:@0.427973:0.716680:0.439244:0.716680:0.439244:0.700211:0.427973:0.700211:0.000000 –3:@0.439250:0.710212:0.450325:0.710212:0.450325:0.700594:0.439250:0.700594:0.000000:0.000000 = (:@0.450324:0.716564:0.475369:0.716564:0.475369:0.700066:0.450324:0.700066:0.000000:0.000000:0.000000:0.000000 A:@0.475369:0.716680:0.486639:0.716680:0.486639:0.700211:0.475369:0.700211:0.000000 –1 3:@0.486638:0.710212:0.508618:0.710212:0.508618:0.700594:0.486638:0.700594:0.000000:0.000000:0.000000:0.000000 ) = :@0.497713:0.716564:0.527711:0.716564:0.527711:0.700066:0.497713:0.700066:0.000000:0.000000:0.000000:0.000000:0.000000 A A A , :@0.527711:0.716680:0.602858:0.716680:0.602858:0.700211:0.527711:0.700211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –1:@0.538979:0.710212:0.550053:0.710212:0.550053:0.700594:0.538979:0.700594:0.000000:0.000000 –1:@0.561323:0.710212:0.572398:0.710212:0.572398:0.700594:0.561323:0.700594:0.000000:0.000000 –1:@0.583668:0.710212:0.594742:0.710212:0.594742:0.700594:0.583668:0.700594:0.000000:0.000000 :@0.602858:0.716564:0.607000:0.716564:0.607000:0.700066:0.602858:0.700066:0.000000 A:@0.641678:0.716680:0.652948:0.716680:0.652948:0.700211:0.641678:0.700211:0.000000 –4:@0.652942:0.710212:0.664017:0.710212:0.664017:0.700594:0.652942:0.700594:0.000000:0.000000 = (:@0.664016:0.716564:0.689060:0.716564:0.689060:0.700066:0.664016:0.700066:0.000000:0.000000:0.000000:0.000000 A:@0.689060:0.716680:0.700331:0.716680:0.700331:0.700211:0.689060:0.700211:0.000000 –1 4:@0.700330:0.710212:0.722310:0.710212:0.722310:0.700594:0.700330:0.700594:0.000000:0.000000:0.000000:0.000000 ) = :@0.711405:0.716564:0.741402:0.716564:0.741402:0.700066:0.711405:0.700066:0.000000:0.000000:0.000000:0.000000:0.000000 A A A A , :@0.741402:0.716680:0.838895:0.716680:0.838895:0.700211:0.741402:0.700211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –1:@0.752673:0.710212:0.763747:0.710212:0.763747:0.700594:0.752673:0.700594:0.000000:0.000000 –1:@0.775015:0.710212:0.786090:0.710212:0.786090:0.700594:0.775015:0.700594:0.000000:0.000000 –1:@0.797360:0.710212:0.808434:0.710212:0.808434:0.700594:0.797360:0.700594:0.000000:0.000000 –1:@0.819704:0.710212:0.830778:0.710212:0.830778:0.700594:0.819704:0.700594:0.000000:0.000000 :@0.404232:0.733915:0.408374:0.733915:0.408374:0.717417:0.404232:0.717417:0.000000 y así, sucesivamente.:@0.427967:0.733915:0.571589:0.733915:0.571589:0.717417:0.427967:0.717417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.404232:0.768992:0.522210:0.768992:0.522210:0.752205:0.404232:0.752205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea la matriz = , calcula .:@0.404232:0.803318:0.699590:0.803318:0.699590:0.786820:0.404232:0.786820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.497206:0.803434:0.508476:0.803434:0.508476:0.786965:0.497206:0.786965:0.000000 A:@0.680608:0.803434:0.691878:0.803434:0.691878:0.786965:0.680608:0.786965:0.000000 2:@0.691882:0.796966:0.696835:0.796966:0.696835:0.787348:0.691882:0.787348:0.000000 :@0.404235:0.820669:0.412519:0.820669:0.412519:0.804171:0.404235:0.804171:0.000000:0.000000 A:@0.404235:0.879965:0.415505:0.879965:0.415505:0.863496:0.404235:0.863496:0.000000 2:@0.415506:0.873497:0.420459:0.873497:0.420459:0.863879:0.415506:0.863879:0.000000 = :@0.420459:0.879849:0.439551:0.879849:0.439551:0.863351:0.420459:0.863351:0.000000:0.000000:0.000000 AA:@0.439551:0.879964:0.462091:0.879964:0.462091:0.863495:0.439551:0.863495:0.000000:0.000000 = = .:@0.462091:0.879849:0.786902:0.879849:0.786902:0.863351:0.462091:0.863351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Saberes previos:@0.199646:0.101880:0.307805:0.101880:0.307805:0.086407:0.199646:0.086407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué es la matriz iden-:@0.199884:0.130507:0.347165:0.130507:0.347165:0.115444:0.199884:0.115444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tidad?:@0.153341:0.146349:0.192531:0.146349:0.192531:0.131286:0.153341:0.131286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desequilibrio cognitivo:@0.199646:0.193880:0.363493:0.193880:0.363493:0.178408:0.199646:0.178408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿A qué es igual el :@0.199884:0.222508:0.313549:0.222508:0.313549:0.207445:0.199884:0.207445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 producto de una matriz por su :@0.153341:0.238350:0.357154:0.238350:0.357154:0.223287:0.153341:0.223287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inversa?:@0.153341:0.254192:0.203525:0.254192:0.203525:0.239129:0.153341:0.239129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Recuerda que…:@0.199646:0.333864:0.309406:0.333864:0.309406:0.318392:0.199646:0.318392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea :@0.199884:0.362493:0.257496:0.362493:0.257496:0.347430:0.199884:0.347430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.225688:0.362599:0.235978:0.362599:0.235978:0.347562:0.225688:0.347562:0.000000 :@0.239759:0.362144:0.253714:0.362144:0.253714:0.349408:0.239759:0.349408:0.000000 M:@0.257496:0.362599:0.271445:0.362599:0.271445:0.347562:0.257496:0.347562:0.000000 2×2 :@0.271445:0.365485:0.288448:0.365485:0.288448:0.356703:0.271445:0.356703:0.000000:0.000000:0.000000:0.000000 [ ]. Si es :@0.288447:0.362493:0.363075:0.362493:0.363075:0.347430:0.288447:0.347430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.293794:0.361490:0.305890:0.361490:0.305890:0.349797:0.293794:0.349797:0.000000 A:@0.332099:0.362599:0.342389:0.362599:0.342389:0.347562:0.332099:0.347562:0.000000 invertible, :@0.153349:0.378335:0.220506:0.378335:0.220506:0.363272:0.153349:0.363272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.220506:0.378441:0.230796:0.378441:0.230796:0.363404:0.220506:0.363404:0.000000 –1:@0.230794:0.372535:0.240905:0.372535:0.240905:0.363753:0.230794:0.363753:0.000000:0.000000 es única. :@0.240904:0.378335:0.303892:0.378335:0.303892:0.363272:0.240904:0.363272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Se dice que es singular si y :@0.153341:0.401306:0.339742:0.401306:0.339742:0.386243:0.153341:0.386243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.231071:0.401412:0.241361:0.401412:0.241361:0.386375:0.231071:0.386375:0.000000 solo si no es invertible, y que :@0.153341:0.417148:0.355906:0.417148:0.355906:0.402085:0.153341:0.402085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.197087:0.417254:0.207377:0.417254:0.207377:0.402217:0.197087:0.402217:0.000000 A:@0.153341:0.433096:0.163631:0.433096:0.163631:0.418059:0.153341:0.418059:0.000000 es no singular si y solo si es :@0.163631:0.432990:0.358051:0.432990:0.358051:0.417927:0.163631:0.417927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.327075:0.433096:0.337366:0.433096:0.337366:0.418059:0.327075:0.418059:0.000000 invertible.:@0.153341:0.448832:0.216716:0.448832:0.216716:0.433769:0.153341:0.433769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La potencia de matrices cumple :@0.153341:0.480516:0.364454:0.480516:0.364454:0.465453:0.153341:0.465453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con las propiedades de los :@0.153341:0.496358:0.328324:0.496358:0.328324:0.481295:0.153341:0.481295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 exponentes.:@0.153341:0.512200:0.231826:0.512200:0.231826:0.497137:0.153341:0.497137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.153341:0.535818:0.160429:0.535818:0.160429:0.520121:0.153341:0.520121:0.000000 Sea :@0.160429:0.535171:0.227580:0.535168:0.227580:0.520105:0.160429:0.520108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.195768:0.535276:0.206058:0.535276:0.206058:0.520240:0.195768:0.520240:0.000000 :@0.209843:0.534819:0.223798:0.534819:0.223798:0.522083:0.209843:0.522083:0.000000 M:@0.227580:0.535274:0.241529:0.535274:0.241529:0.520237:0.227580:0.520237:0.000000 2×2 :@0.241527:0.538161:0.258530:0.538161:0.258530:0.529380:0.241527:0.529380:0.000000:0.000000:0.000000:0.000000 [ ] con ≠ 0. :@0.258531:0.535168:0.355267:0.535168:0.355267:0.520105:0.258531:0.520105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.263878:0.534166:0.275973:0.534166:0.275973:0.522473:0.263878:0.522473:0.000000 A:@0.313491:0.535274:0.323781:0.535274:0.323781:0.520237:0.313491:0.520237:0.000000 Para todo , , :@0.169974:0.551010:0.306503:0.551010:0.306503:0.535947:0.169974:0.535947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.237309:0.551116:0.265664:0.551116:0.265664:0.536079:0.237309:0.536079:0.000000:0.000000:0.000000 :@0.269436:0.550661:0.283391:0.550661:0.283391:0.537925:0.269436:0.537925:0.000000 N:@0.287172:0.550008:0.300205:0.550008:0.300205:0.538315:0.287172:0.538315:0.000000 :@0.153346:0.566852:0.157128:0.566852:0.157128:0.551789:0.153346:0.551789:0.000000 A A:@0.169969:0.566958:0.198352:0.566958:0.198352:0.551921:0.169969:0.551921:0.000000:0.000000:0.000000 m n:@0.180186:0.561115:0.203266:0.561115:0.203266:0.552348:0.180186:0.552348:0.000000:0.000000:0.000000 = :@0.203266:0.566852:0.220698:0.566852:0.220698:0.551789:0.203266:0.551789:0.000000:0.000000:0.000000 A:@0.220698:0.566958:0.230988:0.566958:0.230988:0.551921:0.220698:0.551921:0.000000 m+n:@0.230916:0.561115:0.249570:0.561115:0.249570:0.552348:0.230916:0.552348:0.000000:0.000000:0.000000 .:@0.249570:0.566852:0.252085:0.566852:0.252085:0.551789:0.249570:0.551789:0.000000 (:@0.153352:0.582694:0.175410:0.582694:0.175410:0.567631:0.153352:0.567631:0.000000:0.000000:0.000000 A:@0.175410:0.582800:0.185700:0.582800:0.185700:0.567763:0.175410:0.567763:0.000000 m n:@0.185621:0.576957:0.203916:0.576957:0.203916:0.568190:0.185621:0.568190:0.000000:0.000000:0.000000 ) = :@0.193498:0.582694:0.221348:0.582694:0.221348:0.567631:0.193498:0.567631:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.221348:0.582800:0.231638:0.582800:0.231638:0.567763:0.221348:0.567763:0.000000 mn:@0.231568:0.576957:0.244345:0.576957:0.244345:0.568190:0.231568:0.568190:0.000000:0.000000 .:@0.244345:0.582694:0.246860:0.582694:0.246860:0.567631:0.244345:0.567631:0.000000 •:@0.153351:0.606312:0.160440:0.606312:0.160440:0.590615:0.153351:0.590615:0.000000 Si :@0.160440:0.605665:0.216339:0.605664:0.216339:0.590601:0.160440:0.590602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.184539:0.605771:0.194829:0.605771:0.194829:0.590734:0.184539:0.590734:0.000000 :@0.198602:0.605315:0.212557:0.605315:0.212557:0.592579:0.198602:0.592579:0.000000 M:@0.216339:0.605770:0.230288:0.605770:0.230288:0.590733:0.216339:0.590733:0.000000 2×2 :@0.230288:0.608657:0.247290:0.608657:0.247290:0.599875:0.230288:0.599875:0.000000:0.000000:0.000000:0.000000 [ ] con inver-:@0.247290:0.605664:0.352577:0.605664:0.352577:0.590601:0.247290:0.590601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.252637:0.604661:0.264732:0.604661:0.264732:0.592968:0.252637:0.592968:0.000000 A:@0.302252:0.605770:0.312542:0.605770:0.312542:0.590733:0.302252:0.590733:0.000000 tible, se verifican las propie-:@0.169975:0.621506:0.348512:0.621506:0.348512:0.606443:0.169975:0.606443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dades siguientes: :@0.169975:0.637348:0.281758:0.637348:0.281758:0.622285:0.169975:0.622285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para todo , , :@0.169975:0.653190:0.305452:0.653191:0.305452:0.638128:0.169975:0.638127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.238117:0.653295:0.266472:0.653295:0.266472:0.638259:0.238117:0.638259:0.000000:0.000000:0.000000 :@0.270245:0.652842:0.284200:0.652842:0.284200:0.640106:0.270245:0.640106:0.000000 Z:@0.287981:0.652188:0.299155:0.652188:0.299155:0.640496:0.287981:0.640496:0.000000 :@0.153351:0.669033:0.157133:0.669033:0.157133:0.653970:0.153351:0.653970:0.000000 A A:@0.169974:0.669139:0.198352:0.669139:0.198352:0.654102:0.169974:0.654102:0.000000:0.000000:0.000000 m n:@0.180186:0.663294:0.203266:0.663294:0.203266:0.654528:0.180186:0.654528:0.000000:0.000000:0.000000 = :@0.203266:0.669033:0.220698:0.669033:0.220698:0.653970:0.203266:0.653970:0.000000:0.000000:0.000000 A:@0.220698:0.669139:0.230988:0.669139:0.230988:0.654102:0.220698:0.654102:0.000000 m+n:@0.230916:0.663294:0.249570:0.663294:0.249570:0.654528:0.230916:0.654528:0.000000:0.000000:0.000000 ,:@0.249570:0.669033:0.252085:0.669033:0.252085:0.653970:0.249570:0.653970:0.000000 (:@0.153352:0.684875:0.175410:0.684875:0.175410:0.669812:0.153352:0.669812:0.000000:0.000000:0.000000 A:@0.175410:0.684981:0.185700:0.684981:0.185700:0.669944:0.175410:0.669944:0.000000 m n:@0.185621:0.679136:0.203916:0.679136:0.203916:0.670370:0.185621:0.670370:0.000000:0.000000:0.000000 ) = :@0.193498:0.684875:0.221348:0.684875:0.221348:0.669812:0.193498:0.669812:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.221348:0.684981:0.231638:0.684981:0.231638:0.669944:0.221348:0.669944:0.000000 mn:@0.231568:0.679136:0.244345:0.679136:0.244345:0.670370:0.231568:0.670370:0.000000:0.000000 .:@0.244345:0.684875:0.246860:0.684875:0.246860:0.669812:0.244345:0.669812:0.000000 1:@0.484914:0.377319:0.493410:0.377319:0.493410:0.360821:0.484914:0.360821:0.000000 3:@0.513677:0.377319:0.522173:0.377319:0.522173:0.360821:0.513677:0.360821:0.000000 0:@0.484914:0.398704:0.493410:0.398704:0.493410:0.382206:0.484914:0.382206:0.000000 1:@0.513677:0.398704:0.522173:0.398704:0.522173:0.382206:0.513677:0.382206:0.000000 1 0:@0.617379:0.428992:0.649898:0.428992:0.649898:0.412494:0.617379:0.412494:0.000000:0.000000:0.000000 0 1:@0.617379:0.450377:0.649898:0.450377:0.649898:0.433879:0.617379:0.433879:0.000000:0.000000:0.000000 1 –3:@0.837205:0.428992:0.877354:0.428992:0.877354:0.412494:0.837205:0.412494:0.000000:0.000000:0.000000:0.000000 0 1:@0.837205:0.450377:0.872095:0.450377:0.872095:0.433879:0.837205:0.433879:0.000000:0.000000:0.000000 1 + 0 –3 + 3:@0.453091:0.428992:0.551691:0.428992:0.551691:0.412494:0.453091:0.412494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0 + 0:@0.453091:0.450377:0.489175:0.450377:0.489175:0.433879:0.453091:0.433879:0.000000:0.000000:0.000000:0.000000:0.000000 0 + 1:@0.510348:0.450377:0.546431:0.450377:0.546431:0.433879:0.510348:0.433879:0.000000:0.000000:0.000000:0.000000:0.000000 1 –3:@0.585286:0.377319:0.627804:0.377319:0.627804:0.360821:0.585286:0.360821:0.000000:0.000000:0.000000:0.000000 0:@0.585286:0.398704:0.593782:0.398704:0.593782:0.382206:0.585286:0.382206:0.000000 1:@0.614049:0.398704:0.622545:0.398704:0.622545:0.382206:0.614049:0.382206:0.000000 –:@0.578754:0.790300:0.589254:0.790300:0.589254:0.773802:0.578754:0.773802:0.000000 –:@0.531843:0.866990:0.542343:0.866990:0.542343:0.850492:0.531843:0.850492:0.000000 –:@0.622313:0.866990:0.632813:0.866990:0.632813:0.850492:0.622313:0.850492:0.000000 –:@0.689857:0.866990:0.700357:0.866990:0.700357:0.850492:0.689857:0.850492:0.000000 –:@0.737616:0.866990:0.748115:0.866990:0.748115:0.850492:0.737616:0.850492:0.000000 –:@0.737616:0.899060:0.748115:0.899060:0.748115:0.882562:0.737616:0.882562:0.000000 1:@0.547189:0.782985:0.555685:0.782985:0.555685:0.766487:0.547189:0.766487:0.000000 2:@0.547189:0.799323:0.555685:0.799323:0.555685:0.782826:0.547189:0.782826:0.000000 1:@0.500283:0.859680:0.508779:0.859680:0.508779:0.843183:0.500283:0.843183:0.000000 2:@0.500283:0.876019:0.508779:0.876019:0.508779:0.859521:0.500283:0.859521:0.000000 1:@0.590746:0.859680:0.599242:0.859680:0.599242:0.843183:0.590746:0.843183:0.000000 2:@0.590746:0.876019:0.599242:0.876019:0.599242:0.859521:0.590746:0.859521:0.000000 1:@0.706337:0.859680:0.714833:0.859680:0.714833:0.843183:0.706337:0.843183:0.000000 2:@0.706337:0.876019:0.714833:0.876019:0.714833:0.859521:0.706337:0.859521:0.000000 1:@0.590183:0.814994:0.598679:0.814994:0.598679:0.798497:0.590183:0.798497:0.000000 2:@0.590183:0.831333:0.598679:0.831333:0.598679:0.814835:0.590183:0.814835:0.000000 1:@0.543276:0.891690:0.551772:0.891690:0.551772:0.875192:0.543276:0.875192:0.000000 2:@0.543276:0.908028:0.551772:0.908028:0.551772:0.891531:0.543276:0.891531:0.000000 1:@0.633739:0.891690:0.642235:0.891690:0.642235:0.875192:0.633739:0.875192:0.000000 2:@0.633739:0.908028:0.642235:0.908028:0.642235:0.891531:0.633739:0.891531:0.000000 1:@0.752681:0.891690:0.761177:0.891690:0.761177:0.875192:0.752681:0.875192:0.000000 2:@0.752681:0.908028:0.761177:0.908028:0.761177:0.891531:0.752681:0.891531:0.000000 3:@0.593739:0.782985:0.606474:0.782985:0.606474:0.766487:0.593739:0.766487:0.000000:0.000000 2:@0.595897:0.799323:0.604393:0.799323:0.604393:0.782826:0.595897:0.782826:0.000000 3:@0.546833:0.859680:0.559567:0.859680:0.559567:0.843183:0.546833:0.843183:0.000000:0.000000 2:@0.548990:0.876019:0.557486:0.876019:0.557486:0.859521:0.548990:0.859521:0.000000 3:@0.637296:0.859680:0.650030:0.859680:0.650030:0.843183:0.637296:0.843183:0.000000:0.000000 2:@0.639453:0.876019:0.647949:0.876019:0.647949:0.859521:0.639453:0.859521:0.000000 3:@0.752887:0.859680:0.765621:0.859680:0.765621:0.843183:0.752887:0.843183:0.000000:0.000000 2:@0.755045:0.876019:0.763541:0.876019:0.763541:0.859521:0.755045:0.859521:0.000000 3:@0.545022:0.814994:0.557756:0.814994:0.557756:0.798497:0.545022:0.798497:0.000000:0.000000 2:@0.547179:0.831333:0.555675:0.831333:0.555675:0.814835:0.547179:0.814835:0.000000 3:@0.498115:0.891690:0.510849:0.891690:0.510849:0.875192:0.498115:0.875192:0.000000:0.000000 2:@0.500273:0.908028:0.508769:0.908028:0.508769:0.891531:0.500273:0.891531:0.000000 3:@0.588578:0.891690:0.601312:0.891690:0.601312:0.875192:0.588578:0.875192:0.000000:0.000000 2:@0.590736:0.908028:0.599232:0.908028:0.599232:0.891531:0.590736:0.891531:0.000000 3:@0.702494:0.891690:0.715229:0.891690:0.715229:0.875192:0.702494:0.875192:0.000000:0.000000 2:@0.704652:0.908028:0.713148:0.908028:0.713148:0.891531:0.704652:0.891531:0.000000 Competencia :@0.199748:0.758337:0.297371:0.758337:0.297371:0.742864:0.199748:0.742864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 socioemocional:@0.199748:0.770905:0.310124:0.770905:0.310124:0.755432:0.199748:0.755432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué :@0.199986:0.798251:0.245797:0.798251:0.245797:0.780139:0.199986:0.780139:0.000000:0.000000:0.000000:0.000000:0.000000 crees que :@0.245901:0.797603:0.312361:0.797603:0.312361:0.782389:0.245901:0.782389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 significa que todas las personas :@0.151280:0.816657:0.361978:0.816657:0.361978:0.801443:0.151280:0.801443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tenemos :@0.151280:0.832657:0.213105:0.832657:0.213105:0.817444:0.151280:0.817444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derecho a las mismas :@0.213185:0.832618:0.355926:0.832618:0.355926:0.817555:0.213185:0.817555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 oportunidades?:@0.151268:0.848460:0.254043:0.848460:0.254043:0.833397:0.151268:0.833397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reflexiona:@0.151268:0.864500:0.222066:0.864500:0.222066:0.849239:0.151268:0.849239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sobre esta inte-:@0.222156:0.864302:0.326584:0.864302:0.326584:0.849239:0.222156:0.849239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 rrogante y :@0.151268:0.880144:0.222138:0.880144:0.222138:0.865081:0.151268:0.865081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 debate:@0.222226:0.880342:0.269016:0.880342:0.269016:0.865081:0.222226:0.865081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con tus :@0.269104:0.880144:0.325462:0.880144:0.325462:0.865081:0.269104:0.865081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 compañeros.:@0.151268:0.895986:0.235769:0.895986:0.235769:0.880923:0.151268:0.880923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000