13:@0.921538:0.966074:0.940353:0.966074:0.940353:0.949450:0.921538:0.949450:0.000000:0.000000 Igualdad de matrices:@0.108233:0.097328:0.275485:0.097328:0.275485:0.079645:0.108233:0.079645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición. :@0.108233:0.114498:0.196447:0.114498:0.196447:0.097552:0.108233:0.097552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean = ( ) , = ( ) :@0.196447:0.114035:0.405869:0.114035:0.405869:0.097538:0.196447:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.234245:0.114151:0.245515:0.114151:0.245515:0.097682:0.234245:0.097682:0.000000 a:@0.270560:0.114151:0.279538:0.114151:0.279538:0.097682:0.270560:0.097682:0.000000 ij:@0.279421:0.117381:0.283857:0.117381:0.283857:0.107779:0.279421:0.107779:0.000000:0.000000 2×2:@0.289811:0.117313:0.306018:0.117313:0.306018:0.107695:0.289811:0.107695:0.000000:0.000000:0.000000 B:@0.312914:0.114151:0.322103:0.114151:0.322103:0.097682:0.312914:0.097682:0.000000 b:@0.347148:0.114151:0.356415:0.114151:0.356415:0.097682:0.347148:0.097682:0.000000 ij:@0.356338:0.117381:0.360774:0.117381:0.360774:0.107779:0.356338:0.107779:0.000000:0.000000 2×2:@0.366726:0.117313:0.382933:0.117313:0.382933:0.107695:0.366726:0.107695:0.000000:0.000000:0.000000 :@0.387075:0.113517:0.401728:0.113517:0.401728:0.100143:0.387075:0.100143:0.000000 M:@0.405869:0.114151:0.421146:0.114151:0.421146:0.097682:0.405869:0.097682:0.000000 2×2:@0.421146:0.117313:0.437353:0.117313:0.437353:0.107695:0.421146:0.107695:0.000000:0.000000:0.000000 [ ]. Diremos que las :@0.437354:0.114035:0.587073:0.114035:0.587073:0.097538:0.437354:0.097538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.443211:0.112948:0.456515:0.112948:0.456515:0.100086:0.443211:0.100086:0.000000 matrices y son iguales, y escribiremos = si y solo si = :@0.108236:0.131386:0.571217:0.131386:0.571217:0.114888:0.108236:0.114888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.172390:0.131502:0.208955:0.131502:0.208955:0.115033:0.172390:0.115033:0.000000:0.000000:0.000000 A B:@0.403299:0.131502:0.442851:0.131502:0.442851:0.115033:0.403299:0.115033:0.000000:0.000000:0.000000 a:@0.521068:0.131502:0.530045:0.131502:0.530045:0.115033:0.521068:0.115033:0.000000 ij:@0.529921:0.134731:0.534358:0.134731:0.534358:0.125130:0.529921:0.125130:0.000000:0.000000 b:@0.553451:0.131502:0.562717:0.131502:0.562717:0.115033:0.553451:0.115033:0.000000 ij:@0.562638:0.134731:0.567075:0.134731:0.567075:0.125130:0.562638:0.125130:0.000000:0.000000 i:@0.108234:0.148852:0.112029:0.148852:0.112029:0.132384:0.108234:0.132384:0.000000 = 1, 2, = 1, 2; es decir, = = , = 1, 2, = 1, 2.:@0.112029:0.148737:0.515134:0.148737:0.515134:0.132239:0.112029:0.132239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.170191:0.148852:0.174044:0.148852:0.174044:0.132384:0.170191:0.132384:0.000000 A B:@0.283642:0.148852:0.323194:0.148852:0.323194:0.132384:0.283642:0.132384:0.000000:0.000000:0.000000 ⇔:@0.327331:0.148092:0.346533:0.148092:0.346533:0.131150:0.327331:0.131150:0.000000 a:@0.350675:0.148852:0.359652:0.148852:0.359652:0.132384:0.350675:0.132384:0.000000 ij:@0.359537:0.152082:0.363974:0.152082:0.363974:0.142481:0.359537:0.142481:0.000000:0.000000 b i:@0.383065:0.148852:0.407383:0.148852:0.407383:0.132384:0.383065:0.132384:0.000000:0.000000:0.000000 ij:@0.392255:0.152082:0.396691:0.152082:0.396691:0.142481:0.392255:0.142481:0.000000:0.000000 j:@0.465545:0.148852:0.469398:0.148852:0.469398:0.132384:0.465545:0.132384:0.000000 Ejercicio resuelto:@0.108232:0.183814:0.226211:0.183814:0.226211:0.167027:0.108232:0.167027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108232:0.201006:0.120504:0.201006:0.120504:0.184291:0.108232:0.184291:0.000000:0.000000 Sean las matrices = , = , se tiene que ≠ ,:@0.120504:0.200789:0.588820:0.200789:0.588820:0.184291:0.120504:0.184291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.256111:0.200905:0.267382:0.200905:0.267382:0.184436:0.256111:0.184436:0.000000 B:@0.359643:0.200905:0.368833:0.200905:0.368833:0.184436:0.359643:0.184436:0.000000 A B:@0.546514:0.200905:0.586066:0.200905:0.586066:0.184436:0.546514:0.184436:0.000000:0.000000:0.000000 pues:@0.131966:0.232396:0.165680:0.232396:0.165680:0.215899:0.131966:0.215899:0.000000:0.000000:0.000000:0.000000 a:@0.169822:0.232512:0.178800:0.232512:0.178800:0.216043:0.169822:0.216043:0.000000 22:@0.178809:0.235674:0.188716:0.235674:0.188716:0.226056:0.178809:0.226056:0.000000:0.000000 = –2 y = 2 no son iguales a pesar de que los otros :@0.188715:0.232396:0.570762:0.232396:0.570762:0.215899:0.188715:0.215899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.242908:0.232512:0.252175:0.232512:0.252175:0.216043:0.242908:0.216043:0.000000 22:@0.252175:0.235674:0.262081:0.235674:0.262081:0.226056:0.252175:0.226056:0.000000:0.000000 componentes coinciden.:@0.131982:0.249747:0.307756:0.249747:0.307756:0.233249:0.131982:0.233249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.108247:0.284666:0.120519:0.284666:0.120519:0.267951:0.108247:0.267951:0.000000:0.000000 Sean = , = matrices reales.:@0.120519:0.284449:0.474518:0.284449:0.474518:0.267951:0.120519:0.267951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.169780:0.284564:0.181050:0.284564:0.181050:0.268096:0.169780:0.268096:0.000000 B:@0.273311:0.284564:0.282501:0.284564:0.282501:0.268096:0.273311:0.268096:0.000000 Entonces, = = 4, = –2.:@0.131981:0.316056:0.361648:0.316056:0.361648:0.299558:0.131981:0.299558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.204130:0.316172:0.243681:0.316172:0.243681:0.299703:0.204130:0.299703:0.000000:0.000000:0.000000 ⇔:@0.247817:0.315412:0.267019:0.315412:0.267019:0.298469:0.247817:0.298469:0.000000 x:@0.271159:0.316172:0.278634:0.316172:0.278634:0.299703:0.271159:0.299703:0.000000 y:@0.313119:0.316172:0.320806:0.316172:0.320806:0.299703:0.313119:0.299703:0.000000 Adición en :@0.108233:0.352155:0.199116:0.352155:0.199116:0.334472:0.108233:0.334472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.199116:0.352396:0.215219:0.352396:0.215219:0.334487:0.199116:0.334487:0.000000 2×2:@0.215219:0.355373:0.233479:0.355373:0.233479:0.345064:0.215219:0.345064:0.000000:0.000000:0.000000 [ ]:@0.233479:0.352155:0.261259:0.352155:0.261259:0.334472:0.233479:0.334472:0.000000:0.000000:0.000000 R:@0.240414:0.350543:0.254324:0.350543:0.254324:0.337096:0.240414:0.337096:0.000000 Definición. :@0.108233:0.369325:0.196447:0.369325:0.196447:0.352379:0.108233:0.352379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean = ( ) , = ( ) dos matrices reales.:@0.196447:0.368863:0.523453:0.368863:0.523453:0.352365:0.196447:0.352365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.234245:0.368978:0.245515:0.368978:0.245515:0.352509:0.234245:0.352509:0.000000 a:@0.270560:0.368978:0.279538:0.368978:0.279538:0.352509:0.270560:0.352509:0.000000 ij:@0.279421:0.372207:0.283857:0.372207:0.283857:0.362605:0.279421:0.362605:0.000000:0.000000 2×2:@0.289811:0.372139:0.306018:0.372139:0.306018:0.362521:0.289811:0.362521:0.000000:0.000000:0.000000 B:@0.312914:0.368978:0.322103:0.368978:0.322103:0.352509:0.312914:0.352509:0.000000 b:@0.347148:0.368978:0.356415:0.368978:0.356415:0.352509:0.347148:0.352509:0.000000 ij:@0.356338:0.372207:0.360774:0.372207:0.360774:0.362605:0.356338:0.362605:0.000000:0.000000 2×2:@0.366726:0.372139:0.382933:0.372139:0.382933:0.362521:0.366726:0.362521:0.000000:0.000000:0.000000 i):@0.108231:0.403781:0.118769:0.403781:0.118769:0.387066:0.108231:0.387066:0.000000:0.000000 Definimos la suma de las matrices y como sigue: :@0.118768:0.403564:0.505959:0.403564:0.505959:0.387066:0.118768:0.387066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.376574:0.403680:0.413139:0.403680:0.413139:0.387211:0.376574:0.387211:0.000000:0.000000:0.000000 :@0.108230:0.420915:0.112372:0.420915:0.112372:0.404417:0.108230:0.404417:0.000000 A B:@0.131964:0.421030:0.171516:0.421030:0.171516:0.404562:0.131964:0.404562:0.000000:0.000000:0.000000 + = ( ) + ( ) = ( + ) .:@0.143235:0.420915:0.389522:0.420915:0.389522:0.404417:0.143235:0.404417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.196561:0.421030:0.205539:0.421030:0.205539:0.404562:0.196561:0.404562:0.000000 ij:@0.205434:0.424259:0.209870:0.424259:0.209870:0.414658:0.205434:0.414658:0.000000:0.000000 2×2:@0.215824:0.424191:0.232031:0.424191:0.232031:0.414573:0.215824:0.414573:0.000000:0.000000:0.000000 b:@0.257075:0.421030:0.266341:0.421030:0.266341:0.404562:0.257075:0.404562:0.000000 ij:@0.266263:0.424259:0.270700:0.424259:0.270700:0.414658:0.266263:0.414658:0.000000:0.000000 2×2:@0.276653:0.424191:0.292861:0.424191:0.292861:0.414573:0.276653:0.414573:0.000000:0.000000:0.000000 a:@0.317904:0.421030:0.326882:0.421030:0.326882:0.404562:0.317904:0.404562:0.000000 ij :@0.326766:0.424259:0.336032:0.424259:0.336032:0.414658:0.326766:0.414658:0.000000:0.000000:0.000000:0.000000 b:@0.350982:0.421030:0.360249:0.421030:0.360249:0.404562:0.350982:0.404562:0.000000 ij:@0.360171:0.424259:0.364607:0.424259:0.364607:0.414658:0.360171:0.414658:0.000000:0.000000 2×2:@0.370559:0.424191:0.386766:0.424191:0.386766:0.414573:0.370559:0.414573:0.000000:0.000000:0.000000 :@0.108230:0.438266:0.112372:0.438266:0.112372:0.421768:0.108230:0.421768:0.000000 ii):@0.108230:0.455833:0.123025:0.455833:0.123025:0.439119:0.108230:0.439119:0.000000:0.000000:0.000000 La operación adición “+\ en :@0.123025:0.455616:0.332206:0.455616:0.332206:0.439119:0.123025:0.439119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.332206:0.455732:0.347483:0.455732:0.347483:0.439263:0.332206:0.439263:0.000000 2×2:@0.347494:0.458893:0.363701:0.458893:0.363701:0.449275:0.347494:0.449275:0.000000:0.000000:0.000000 [ ] es la función definida como::@0.363700:0.455616:0.593003:0.455616:0.593003:0.439119:0.363700:0.439119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.369557:0.454529:0.382862:0.454529:0.382862:0.441667:0.369557:0.441667:0.000000 :@0.108235:0.487224:0.112377:0.487224:0.112377:0.470726:0.108235:0.470726:0.000000 +: . :@0.131970:0.487224:0.392667:0.487224:0.392667:0.470726:0.131970:0.470726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108235:0.521925:0.112377:0.521925:0.112377:0.505427:0.108235:0.505427:0.000000 Si las matrices reales = ( ) , = ( ) se escriben:@0.131970:0.521925:0.508839:0.521924:0.508839:0.505426:0.131970:0.505427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.277904:0.522041:0.289174:0.522041:0.289174:0.505572:0.277904:0.505572:0.000000 a:@0.314219:0.522041:0.323196:0.522041:0.323196:0.505572:0.314219:0.505572:0.000000 ij:@0.323086:0.525269:0.327522:0.525269:0.327522:0.515668:0.323086:0.515668:0.000000:0.000000 2×2:@0.333474:0.525202:0.349681:0.525202:0.349681:0.515584:0.333474:0.515584:0.000000:0.000000:0.000000 B:@0.356579:0.522040:0.365768:0.522040:0.365768:0.505571:0.356579:0.505571:0.000000 b:@0.390813:0.522040:0.400080:0.522040:0.400080:0.505571:0.390813:0.505571:0.000000 ij:@0.400001:0.525269:0.404438:0.525269:0.404438:0.515668:0.400001:0.515668:0.000000:0.000000 2×2:@0.410389:0.525202:0.426597:0.525202:0.426597:0.515584:0.410389:0.515584:0.000000:0.000000:0.000000 como = , = , la suma de estas dos :@0.131973:0.558881:0.544284:0.558881:0.544284:0.542383:0.131973:0.542383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.177901:0.558997:0.189171:0.558997:0.189171:0.542528:0.177901:0.542528:0.000000 B:@0.289717:0.558997:0.298906:0.558997:0.298906:0.542528:0.289717:0.542528:0.000000 :@0.108239:0.600711:0.112381:0.600711:0.112381:0.584214:0.108239:0.584214:0.000000 matrices se expresa como::@0.131973:0.600711:0.317187:0.600711:0.317187:0.584214:0.131973:0.584214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108239:0.635413:0.112381:0.635413:0.112381:0.618915:0.108239:0.618915:0.000000 A B:@0.131973:0.635529:0.171524:0.635529:0.171524:0.619060:0.131973:0.619060:0.000000:0.000000:0.000000 + = + = .:@0.143243:0.635413:0.517355:0.635413:0.517355:0.618915:0.143243:0.618915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Nota que la adición de dos matrices de 2 × 2 es una matriz de 2 × 2 :@0.108238:0.677243:0.600003:0.677243:0.600003:0.660745:0.108238:0.660745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que se obtiene sumando sus respectivos componentes.:@0.108238:0.694593:0.500223:0.694593:0.500223:0.678096:0.108238:0.678096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicios resueltos:@0.108238:0.729671:0.238893:0.729671:0.238893:0.712884:0.108238:0.712884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108238:0.759341:0.120510:0.759341:0.120510:0.742626:0.108238:0.742626:0.000000:0.000000 Sean = , = , entonces, :@0.120511:0.759124:0.442471:0.759124:0.442471:0.742626:0.120511:0.742626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.169771:0.759239:0.181041:0.759239:0.181041:0.742771:0.169771:0.742771:0.000000 B:@0.273303:0.759239:0.282492:0.759239:0.282492:0.742771:0.273303:0.742771:0.000000 :@0.108239:0.809860:0.112381:0.809860:0.112381:0.793362:0.108239:0.793362:0.000000 A B:@0.131973:0.809975:0.171524:0.809975:0.171524:0.793507:0.131973:0.793507:0.000000:0.000000:0.000000 + = + = = .:@0.143243:0.809860:0.586151:0.809860:0.586151:0.793362:0.143243:0.793362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.108238:0.864384:0.120510:0.864384:0.120510:0.847670:0.108238:0.847670:0.000000:0.000000 Sea = con :@0.120511:0.864167:0.287962:0.864167:0.287962:0.847670:0.120511:0.847670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.160235:0.864283:0.171505:0.864283:0.171505:0.847814:0.160235:0.847814:0.000000 a, b, c, d:@0.287962:0.864283:0.342962:0.864283:0.342962:0.847814:0.287962:0.847814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Entonces, :@0.342962:0.864167:0.458252:0.864157:0.458252:0.847660:0.342962:0.847670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.347109:0.863639:0.361761:0.863639:0.361761:0.850266:0.347109:0.850266:0.000000 R:@0.365903:0.863070:0.379208:0.863070:0.379208:0.850208:0.365903:0.850208:0.000000 :@0.108241:0.914894:0.112383:0.914894:0.112383:0.898396:0.108241:0.898396:0.000000 A:@0.131976:0.915010:0.143246:0.915010:0.143246:0.898541:0.131976:0.898541:0.000000 + 0 = + = = = .:@0.143246:0.914894:0.592125:0.914894:0.592125:0.898396:0.143246:0.898396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.578100:0.915010:0.589370:0.915010:0.589370:0.898541:0.578100:0.898541:0.000000 Recuerda que…:@0.684804:0.142113:0.794564:0.142113:0.794564:0.126641:0.684804:0.126641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La definición establece :@0.685042:0.170741:0.836488:0.170741:0.836488:0.155678:0.685042:0.155678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que dos matrices de :@0.638498:0.186583:0.772744:0.186583:0.772744:0.171520:0.638498:0.171520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.772744:0.186688:0.786692:0.186688:0.786692:0.171652:0.772744:0.171652:0.000000 2×2:@0.786697:0.189576:0.801495:0.189576:0.801495:0.180794:0.786697:0.180794:0.000000:0.000000:0.000000 [ ] :@0.801496:0.186583:0.831848:0.186583:0.831848:0.171520:0.801496:0.171520:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.806842:0.185580:0.818937:0.185580:0.818937:0.173887:0.806842:0.173887:0.000000 son iguales, si y solo si sus :@0.638498:0.202425:0.807218:0.202425:0.807218:0.187362:0.638498:0.187362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 respectivos componentes son :@0.638498:0.218267:0.836453:0.218267:0.836453:0.203204:0.638498:0.203204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 iguales. La negación de la igual-:@0.638498:0.234109:0.840043:0.234109:0.840043:0.219046:0.638498:0.219046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dad de matrices en :@0.638498:0.249951:0.765692:0.249951:0.765692:0.234888:0.638498:0.234888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.765692:0.250056:0.779641:0.250056:0.779641:0.235020:0.765692:0.235020:0.000000 2×2:@0.779644:0.252944:0.794442:0.252944:0.794442:0.244162:0.779644:0.244162:0.000000:0.000000:0.000000 [ ] se :@0.794441:0.249951:0.838093:0.249951:0.838093:0.234888:0.794441:0.234888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.799789:0.248948:0.811884:0.248948:0.811884:0.237255:0.799789:0.237255:0.000000 establece del modo siguiente: :@0.638499:0.265793:0.833674:0.265793:0.833674:0.250730:0.638499:0.250730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sean = ( ), = ( ) dos ma-:@0.638499:0.281635:0.834218:0.281635:0.834218:0.266572:0.638499:0.266572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.671393:0.281740:0.681683:0.281740:0.681683:0.266704:0.671393:0.266704:0.000000 a B:@0.704550:0.281740:0.736818:0.281740:0.736818:0.266704:0.704550:0.266704:0.000000:0.000000:0.000000 ij:@0.712644:0.284689:0.716695:0.284689:0.716695:0.275923:0.712644:0.275923:0.000000:0.000000 b:@0.759685:0.281740:0.768146:0.281740:0.768146:0.266704:0.759685:0.266704:0.000000 ij:@0.768075:0.284689:0.772126:0.284689:0.772126:0.275923:0.768075:0.275923:0.000000:0.000000 trices de :@0.638512:0.297477:0.696735:0.297477:0.696735:0.282414:0.638512:0.282414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.696735:0.297582:0.710684:0.297582:0.710684:0.282546:0.696735:0.282546:0.000000 2×2:@0.710674:0.300470:0.725472:0.300470:0.725472:0.291688:0.710674:0.291688:0.000000:0.000000:0.000000 [ ], entonces, :@0.725472:0.297477:0.820170:0.297477:0.820170:0.282414:0.725472:0.282414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.730819:0.296474:0.742914:0.296474:0.742914:0.284781:0.730819:0.284781:0.000000 A B:@0.638500:0.313424:0.674612:0.313424:0.674612:0.298388:0.638500:0.298388:0.000000:0.000000:0.000000 ≠ ≠ para algún :@0.648790:0.313319:0.815516:0.313319:0.815516:0.298256:0.648790:0.298256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.678398:0.312718:0.695854:0.312718:0.695854:0.297316:0.678398:0.297316:0.000000 a:@0.699635:0.313424:0.707832:0.313424:0.707832:0.298388:0.699635:0.298388:0.000000 ij:@0.707726:0.316373:0.711777:0.316373:0.711777:0.307607:0.707726:0.307607:0.000000:0.000000 b:@0.729208:0.313424:0.737669:0.313424:0.737669:0.298388:0.729208:0.298388:0.000000 ij :@0.737599:0.316373:0.743854:0.316373:0.743854:0.307607:0.737599:0.307607:0.000000:0.000000:0.000000 índice y . Es decir que dos :@0.638508:0.329161:0.818541:0.329161:0.818541:0.314098:0.638508:0.314098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i j:@0.681410:0.329266:0.703098:0.329266:0.703098:0.314230:0.681410:0.314230:0.000000:0.000000:0.000000 matrices de :@0.638508:0.345003:0.717170:0.345003:0.717170:0.329940:0.638508:0.329940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M:@0.717170:0.345108:0.731119:0.345108:0.731119:0.330072:0.717170:0.330072:0.000000 2×2:@0.731114:0.347996:0.745912:0.347996:0.745912:0.339214:0.731114:0.339214:0.000000:0.000000:0.000000 no son iguales, :@0.745911:0.345003:0.848213:0.345003:0.848213:0.329940:0.745911:0.329940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si y solo si, al menos uno de los :@0.638507:0.360845:0.842848:0.360845:0.842848:0.345782:0.638507:0.345782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 respectivos componentes es :@0.638507:0.376687:0.826117:0.376687:0.826117:0.361624:0.638507:0.361624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 distinto.:@0.638507:0.392529:0.690327:0.392529:0.690327:0.377466:0.638507:0.377466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad:@0.684804:0.511784:0.831589:0.511784:0.831589:0.496311:0.684804:0.496311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Física:@0.685042:0.540834:0.813762:0.540834:0.813762:0.525361:0.685042:0.525361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las matrices se presentan en :@0.638498:0.556253:0.826902:0.556253:0.826902:0.541190:0.638498:0.541190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una variedad de campos. Se :@0.638498:0.572095:0.823172:0.572095:0.823172:0.557032:0.638498:0.557032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aplican, por ejemplo, en la física, :@0.638498:0.587937:0.849311:0.587937:0.849311:0.572874:0.638498:0.572874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la química, la biología, en las :@0.638498:0.603779:0.824933:0.603779:0.824933:0.588716:0.638498:0.588716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 distintas ramas de la ingeniería, :@0.638498:0.619621:0.842611:0.619621:0.842611:0.604558:0.638498:0.604558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en la economía, la administra-:@0.638498:0.635463:0.832690:0.635463:0.832690:0.620400:0.638498:0.620400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción de empresas, en sociología, :@0.638498:0.651305:0.849665:0.651305:0.849665:0.636242:0.638498:0.636242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en los problemas ambientales, :@0.638498:0.667147:0.837470:0.667147:0.837470:0.652084:0.638498:0.652084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y en las distintas ramas de las :@0.638498:0.682989:0.830437:0.682989:0.830437:0.667926:0.638498:0.667926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemáticas.:@0.638498:0.698831:0.724250:0.698831:0.724250:0.683768:0.638498:0.683768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.638503:0.866944:0.649984:0.866944:0.649984:0.856920:0.638503:0.856920:0.000000 :@0.649984:0.867652:0.652865:0.867652:0.652865:0.856175:0.649984:0.856175:0.000000 Túnel de números binarios.:@0.652865:0.867652:0.786307:0.867652:0.786307:0.856175:0.652865:0.856175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Confecciona:@0.638503:0.887212:0.722742:0.887212:0.722742:0.871951:0.638503:0.871951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un resumen acer-:@0.722742:0.887014:0.839065:0.887014:0.839065:0.871951:0.722742:0.871951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ca del uso de las matrices en la :@0.638503:0.902856:0.840593:0.902856:0.840593:0.887793:0.638503:0.887793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vida cotidiana.:@0.638503:0.918698:0.732047:0.918698:0.732047:0.903635:0.638503:0.903635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Shutterstock, 594116819:@0.871305:0.846462:0.871305:0.778288:0.859836:0.778288:0.859836:0.846462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 –1:@0.297629:0.190445:0.340147:0.190445:0.340147:0.173948:0.297629:0.173948:0.000000:0.000000:0.000000:0.000000 1 –2:@0.297629:0.211830:0.340147:0.211830:0.340147:0.195332:0.297629:0.195332:0.000000:0.000000:0.000000:0.000000 4:@0.211101:0.274578:0.219597:0.274578:0.219597:0.258080:0.211101:0.258080:0.000000 0:@0.239864:0.274578:0.248360:0.274578:0.248360:0.258080:0.239864:0.258080:0.000000 –2 3:@0.205842:0.295962:0.248360:0.295962:0.248360:0.279465:0.205842:0.279465:0.000000:0.000000:0.000000:0.000000 2 –1:@0.398143:0.190445:0.440662:0.190445:0.440662:0.173948:0.398143:0.173948:0.000000:0.000000:0.000000:0.000000 1:@0.398143:0.211830:0.406639:0.211830:0.406639:0.195332:0.398143:0.195332:0.000000 2:@0.426906:0.211830:0.435402:0.211830:0.435402:0.195332:0.426906:0.195332:0.000000 x:@0.312126:0.274693:0.319601:0.274693:0.319601:0.258224:0.312126:0.258224:0.000000 0:@0.340389:0.274578:0.348885:0.274578:0.348885:0.258080:0.340389:0.258080:0.000000 y:@0.312030:0.296078:0.319717:0.296078:0.319717:0.279609:0.312030:0.279609:0.000000 3:@0.340389:0.295962:0.348885:0.295962:0.348885:0.279465:0.340389:0.279465:0.000000 M:@0.164729:0.477806:0.180006:0.477806:0.180006:0.461338:0.164729:0.461338:0.000000 2×2:@0.180007:0.480969:0.196214:0.480969:0.196214:0.471351:0.180007:0.471351:0.000000:0.000000:0.000000 [ ] × :@0.196213:0.477691:0.240323:0.477691:0.240323:0.461193:0.196213:0.461193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.202070:0.476604:0.215375:0.476604:0.215375:0.463742:0.202070:0.463742:0.000000 M:@0.240323:0.477806:0.255601:0.477806:0.255601:0.461338:0.240323:0.461338:0.000000 2×2:@0.255599:0.480969:0.271806:0.480969:0.271806:0.471351:0.255599:0.471351:0.000000:0.000000:0.000000 [ ] :@0.271807:0.477691:0.321252:0.477691:0.321252:0.461193:0.271807:0.461193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.277663:0.476604:0.290968:0.476604:0.290968:0.463742:0.277663:0.463742:0.000000 →:@0.300965:0.485790:0.317109:0.485790:0.317109:0.465927:0.300965:0.465927:0.000000 M:@0.321252:0.477806:0.336529:0.477806:0.336529:0.461338:0.321252:0.461338:0.000000 2×2:@0.336526:0.480969:0.352734:0.480969:0.352734:0.471351:0.336526:0.471351:0.000000:0.000000:0.000000 [ ]:@0.352734:0.477691:0.377751:0.477691:0.377751:0.461193:0.352734:0.461193:0.000000:0.000000:0.000000 R:@0.358591:0.476604:0.371896:0.476604:0.371896:0.463742:0.358591:0.463742:0.000000 ( , ) + :@0.257343:0.495042:0.351396:0.495042:0.351396:0.478544:0.257343:0.478544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.263296:0.495157:0.290652:0.495157:0.290652:0.478688:0.263296:0.478688:0.000000:0.000000:0.000000 →:@0.300747:0.503140:0.316892:0.503140:0.316892:0.483278:0.300747:0.483278:0.000000 A B:@0.321034:0.495157:0.360585:0.495157:0.360585:0.478688:0.321034:0.478688:0.000000:0.000000:0.000000 a:@0.215708:0.549260:0.224686:0.549260:0.224686:0.532791:0.215708:0.532791:0.000000 11:@0.224686:0.552421:0.234592:0.552421:0.234592:0.542803:0.224686:0.542803:0.000000:0.000000 a:@0.249226:0.549260:0.258204:0.549260:0.258204:0.532791:0.249226:0.532791:0.000000 12:@0.258204:0.552421:0.268110:0.552421:0.268110:0.542803:0.258204:0.542803:0.000000:0.000000 a:@0.215708:0.570644:0.224686:0.570644:0.224686:0.554176:0.215708:0.554176:0.000000 21:@0.224686:0.573805:0.234592:0.573805:0.234592:0.564187:0.224686:0.564187:0.000000:0.000000 a:@0.249226:0.570644:0.258204:0.570644:0.258204:0.554176:0.249226:0.554176:0.000000 22:@0.258204:0.573805:0.268110:0.573805:0.268110:0.564187:0.258204:0.564187:0.000000:0.000000 a:@0.197280:0.624282:0.206258:0.624282:0.206258:0.607813:0.197280:0.607813:0.000000 11:@0.206258:0.627444:0.216164:0.627444:0.216164:0.617826:0.206258:0.617826:0.000000:0.000000 a:@0.230799:0.624282:0.239776:0.624282:0.239776:0.607813:0.230799:0.607813:0.000000 12:@0.239776:0.627444:0.249683:0.627444:0.249683:0.617826:0.239776:0.617826:0.000000:0.000000 a:@0.197280:0.645666:0.206258:0.645666:0.206258:0.629197:0.197280:0.629197:0.000000 21:@0.206258:0.648827:0.216164:0.648827:0.216164:0.639209:0.206258:0.639209:0.000000:0.000000 a:@0.230799:0.645666:0.239776:0.645666:0.239776:0.629197:0.230799:0.629197:0.000000 22:@0.239776:0.648827:0.249683:0.648827:0.249683:0.639209:0.239776:0.639209:0.000000:0.000000 a:@0.368017:0.624282:0.376995:0.624282:0.376995:0.607813:0.368017:0.607813:0.000000 11:@0.376995:0.627444:0.386901:0.627444:0.386901:0.617826:0.376995:0.617826:0.000000:0.000000 + :@0.386901:0.624166:0.405993:0.624166:0.405993:0.607669:0.386901:0.607669:0.000000:0.000000:0.000000 b:@0.405993:0.624282:0.415259:0.624282:0.415259:0.607813:0.405993:0.607813:0.000000 11:@0.415259:0.627444:0.425166:0.627444:0.425166:0.617826:0.415259:0.617826:0.000000:0.000000 a:@0.448746:0.624282:0.457723:0.624282:0.457723:0.607813:0.448746:0.607813:0.000000 12:@0.457723:0.627444:0.467630:0.627444:0.467630:0.617826:0.457723:0.617826:0.000000:0.000000 + :@0.467629:0.624166:0.486721:0.624166:0.486721:0.607669:0.467629:0.607669:0.000000:0.000000:0.000000 b:@0.486721:0.624282:0.495987:0.624282:0.495987:0.607813:0.486721:0.607813:0.000000 12:@0.495987:0.627444:0.505894:0.627444:0.505894:0.617826:0.495987:0.617826:0.000000:0.000000 a:@0.368017:0.645666:0.376995:0.645666:0.376995:0.629197:0.368017:0.629197:0.000000 21:@0.376995:0.648827:0.386901:0.648827:0.386901:0.639209:0.376995:0.639209:0.000000:0.000000 + :@0.386901:0.645551:0.405993:0.645551:0.405993:0.629053:0.386901:0.629053:0.000000:0.000000:0.000000 b:@0.405993:0.645666:0.415259:0.645666:0.415259:0.629197:0.405993:0.629197:0.000000 21:@0.415259:0.648827:0.425166:0.648827:0.425166:0.639209:0.415259:0.639209:0.000000:0.000000 a:@0.448746:0.645666:0.457723:0.645666:0.457723:0.629197:0.448746:0.629197:0.000000 22:@0.457723:0.648827:0.467630:0.648827:0.467630:0.639209:0.457723:0.639209:0.000000:0.000000 + :@0.467629:0.645551:0.486721:0.645551:0.486721:0.629053:0.467629:0.629053:0.000000:0.000000:0.000000 b:@0.486721:0.645666:0.495987:0.645666:0.495987:0.629197:0.486721:0.629197:0.000000 22:@0.495987:0.648827:0.505894:0.648827:0.505894:0.639209:0.495987:0.639209:0.000000:0.000000 b:@0.326130:0.549260:0.335396:0.549260:0.335396:0.532791:0.326130:0.532791:0.000000 11:@0.335396:0.552421:0.345302:0.552421:0.345302:0.542803:0.335396:0.542803:0.000000:0.000000 b:@0.359646:0.549260:0.368913:0.549260:0.368913:0.532791:0.359646:0.532791:0.000000 12:@0.368914:0.552421:0.378820:0.552421:0.378820:0.542803:0.368914:0.542803:0.000000:0.000000 b:@0.326130:0.570644:0.335396:0.570644:0.335396:0.554176:0.326130:0.554176:0.000000 21:@0.335396:0.573805:0.345302:0.573805:0.345302:0.564187:0.335396:0.564187:0.000000:0.000000 b:@0.359646:0.570644:0.368913:0.570644:0.368913:0.554176:0.359646:0.554176:0.000000 22:@0.368914:0.573805:0.378820:0.573805:0.378820:0.564187:0.368914:0.564187:0.000000:0.000000 b:@0.282574:0.624282:0.291840:0.624282:0.291840:0.607813:0.282574:0.607813:0.000000 11:@0.291839:0.627444:0.301746:0.627444:0.301746:0.617826:0.291839:0.617826:0.000000:0.000000 b:@0.316090:0.624282:0.325357:0.624282:0.325357:0.607813:0.316090:0.607813:0.000000 12:@0.325358:0.627444:0.335264:0.627444:0.335264:0.617826:0.325358:0.617826:0.000000:0.000000 b:@0.282574:0.645666:0.291840:0.645666:0.291840:0.629197:0.282574:0.629197:0.000000 21:@0.291839:0.648827:0.301746:0.648827:0.301746:0.639209:0.291839:0.639209:0.000000:0.000000 b:@0.316090:0.645666:0.325357:0.645666:0.325357:0.629197:0.316090:0.629197:0.000000 22:@0.325358:0.648827:0.335264:0.648827:0.335264:0.639209:0.325358:0.639209:0.000000:0.000000 3:@0.212632:0.748749:0.221128:0.748749:0.221128:0.732251:0.212632:0.732251:0.000000 5:@0.241395:0.748749:0.249891:0.748749:0.249891:0.732251:0.241395:0.732251:0.000000 –8 12:@0.207373:0.770133:0.254130:0.770133:0.254130:0.753636:0.207373:0.753636:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.200979:0.854398:0.209957:0.854398:0.209957:0.837930:0.200979:0.837930:0.000000 b:@0.229608:0.854398:0.238874:0.854398:0.238874:0.837930:0.229608:0.837930:0.000000 c:@0.201885:0.875783:0.209071:0.875783:0.209071:0.859314:0.201885:0.859314:0.000000 d:@0.229665:0.875783:0.238836:0.875783:0.238836:0.859314:0.229665:0.859314:0.000000 a:@0.200979:0.905739:0.209957:0.905739:0.209957:0.889270:0.200979:0.889270:0.000000 b:@0.229608:0.905739:0.238874:0.905739:0.238874:0.889270:0.229608:0.889270:0.000000 c:@0.201885:0.927124:0.209071:0.927124:0.209071:0.910655:0.201885:0.910655:0.000000 d:@0.229665:0.927124:0.238836:0.927124:0.238836:0.910655:0.229665:0.910655:0.000000 a:@0.512353:0.905739:0.521330:0.905739:0.521330:0.889270:0.512353:0.889270:0.000000 b:@0.540981:0.905739:0.550248:0.905739:0.550248:0.889270:0.540981:0.889270:0.000000 c:@0.513258:0.927124:0.520444:0.927124:0.520444:0.910655:0.513258:0.910655:0.000000 d:@0.541039:0.927124:0.550209:0.927124:0.550209:0.910655:0.541039:0.910655:0.000000 0:@0.277967:0.905623:0.286463:0.905623:0.286463:0.889126:0.277967:0.889126:0.000000 0:@0.306730:0.905623:0.315226:0.905623:0.315226:0.889126:0.306730:0.889126:0.000000 0:@0.277967:0.927008:0.286463:0.927008:0.286463:0.910510:0.277967:0.910510:0.000000 0:@0.306730:0.927008:0.315226:0.927008:0.315226:0.910510:0.306730:0.910510:0.000000 3:@0.200906:0.799545:0.209402:0.799545:0.209402:0.783047:0.200906:0.783047:0.000000 5:@0.229669:0.799545:0.238165:0.799545:0.238165:0.783047:0.229669:0.783047:0.000000 –8 12:@0.195646:0.820930:0.242403:0.820930:0.242403:0.804432:0.195646:0.804432:0.000000:0.000000:0.000000:0.000000:0.000000 –1 4:@0.307896:0.748749:0.350415:0.748749:0.350415:0.732251:0.307896:0.732251:0.000000:0.000000:0.000000:0.000000 10 15:@0.308898:0.770133:0.354653:0.770133:0.354653:0.753636:0.308898:0.753636:0.000000:0.000000:0.000000:0.000000:0.000000 –1 4:@0.272716:0.799545:0.315235:0.799545:0.315235:0.783047:0.272716:0.783047:0.000000:0.000000:0.000000:0.000000 10 15:@0.273718:0.820930:0.319473:0.820930:0.319473:0.804432:0.273718:0.804432:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.531588:0.799545:0.540084:0.799545:0.540084:0.783047:0.531588:0.783047:0.000000 9:@0.560351:0.799545:0.568847:0.799545:0.568847:0.783047:0.560351:0.783047:0.000000 2 27:@0.531588:0.820930:0.573105:0.820930:0.573105:0.804432:0.531588:0.804432:0.000000:0.000000:0.000000:0.000000 3 – 1:@0.368232:0.799545:0.404008:0.799545:0.404008:0.783047:0.368232:0.783047:0.000000:0.000000:0.000000:0.000000:0.000000 5 + 4:@0.444330:0.799545:0.480414:0.799545:0.480414:0.783047:0.444330:0.783047:0.000000:0.000000:0.000000:0.000000:0.000000 –8 + 10:@0.358580:0.820930:0.413659:0.820930:0.413659:0.804432:0.358580:0.804432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 12 + 15:@0.435834:0.820930:0.488909:0.820930:0.488909:0.804432:0.435834:0.804432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.363089:0.905739:0.372067:0.905739:0.372067:0.889270:0.363089:0.889270:0.000000 + 0:@0.372067:0.905623:0.399654:0.905623:0.399654:0.889126:0.372067:0.889126:0.000000:0.000000:0.000000:0.000000 b:@0.429708:0.905739:0.438975:0.905739:0.438975:0.889270:0.429708:0.889270:0.000000 + 0:@0.438975:0.905623:0.466563:0.905623:0.466563:0.889126:0.438975:0.889126:0.000000:0.000000:0.000000:0.000000 c:@0.363994:0.927124:0.371180:0.927124:0.371180:0.910655:0.363994:0.910655:0.000000 + 0:@0.371180:0.927008:0.398768:0.927008:0.398768:0.910510:0.371180:0.910510:0.000000:0.000000:0.000000:0.000000 d:@0.429766:0.927124:0.438936:0.927124:0.438936:0.910655:0.429766:0.910655:0.000000 + 0:@0.438936:0.927008:0.466524:0.927008:0.466524:0.910510:0.438936:0.910510:0.000000:0.000000:0.000000:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción 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