156:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
M.5.2.7. Calcular el producto escalar entre dos vectores y la norma de un vector para determinar la distancia entre dos puntos   y   en :@0.143847:0.948432:0.716156:0.948432:0.716156:0.938390:0.143847:0.938390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.677351:0.948502:0.700454:0.948502:0.700454:0.938478:0.677351:0.938478:0.000000:0.000000:0.000000
R:@0.716836:0.947842:0.725303:0.947842:0.725303:0.939657:0.716836:0.939657:0.000000
2:@0.725053:0.944565:0.728068:0.944565:0.728068:0.938711:0.725053:0.938711:0.000000
 como la norma del vector :@0.727931:0.948432:0.844132:0.948432:0.844132:0.938390:0.727931:0.938390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.844812:0.948502:0.856961:0.948502:0.856961:0.938478:0.844812:0.938478:0.000000:0.000000
. M.5.2.8. :@0.856713:0.948432:0.894297:0.948432:0.894297:0.938390:0.856713:0.938390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconocer que dos vectores son ortogonales cuando su producto escalar es cero y aplicar el teorema de Pitágoras para resolver y plantear aplicaciones geométricas con operaciones y :@0.143849:0.957233:0.894319:0.957233:0.894319:0.947191:0.143849:0.947191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elementos en  , apoyándose en el uso de las TIC (:@0.143849:0.966034:0.353440:0.966034:0.353440:0.955992:0.143849:0.955992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.201438:0.965444:0.209905:0.965444:0.209905:0.957259:0.201438:0.957259:0.000000
2:@0.209667:0.962167:0.212682:0.962167:0.212682:0.956313:0.209667:0.956313:0.000000
software :@0.353206:0.966104:0.389827:0.966104:0.389827:0.956080:0.353206:0.956080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como GeoGebra, calculadora gráfica, :@0.389595:0.966034:0.544550:0.966034:0.544550:0.955992:0.389595:0.955992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
applets:@0.544315:0.966104:0.573550:0.966104:0.573550:0.956080:0.544315:0.956080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 e Internet).:@0.573316:0.966034:0.620364:0.966034:0.620364:0.955992:0.573316:0.955992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Producto escalar, norma y vectores :@0.404235:0.094560:0.849563:0.094560:0.849563:0.049901:0.404235:0.049901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ortogonales en :@0.404235:0.132279:0.595363:0.132279:0.595363:0.087620:0.404235:0.087620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.595363:0.130280:0.631648:0.130280:0.631648:0.095202:0.595363:0.095202:0.000000
2:@0.631658:0.115928:0.640331:0.115928:0.640331:0.089892:0.631658:0.089892:0.000000
Saberes previos:@0.199646:0.103163:0.307805:0.103163:0.307805:0.087691:0.199646:0.087691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el enunciado :@0.199884:0.131792:0.342187:0.131792:0.342187:0.116729:0.199884:0.116729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del teorema de Pitágoras?:@0.153341:0.147634:0.319244:0.147634:0.319244:0.132571:0.153341:0.132571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199644:0.191221:0.363492:0.191221:0.363492:0.175749:0.199644:0.175749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo pruebas que dos :@0.199880:0.219849:0.361107:0.219849:0.361107:0.204785:0.199880:0.204785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectores son ortogonales?:@0.153337:0.235691:0.321248:0.235691:0.321248:0.220627:0.153337:0.220627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En esta sección, estudiaremos el espacio vectorial :@0.404236:0.154497:0.760965:0.154497:0.760965:0.137999:0.404236:0.137999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.761774:0.153528:0.775684:0.153528:0.775684:0.140081:0.761774:0.140081:0.000000
2:@0.775694:0.148144:0.780647:0.148144:0.780647:0.138525:0.775694:0.138525:0.000000
 que posee una :@0.780646:0.154497:0.895906:0.154497:0.895906:0.137999:0.780646:0.137999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estructura adicional conocida como espacio con producto escalar, :@0.404241:0.171847:0.895865:0.171847:0.895865:0.155350:0.404241:0.155350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto interno o producto punto.:@0.404241:0.189198:0.664802:0.189198:0.664802:0.172700:0.404241:0.172700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Producto escalar en :@0.404236:0.225297:0.567387:0.225297:0.567387:0.207614:0.404236:0.207614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.567387:0.223803:0.581901:0.223803:0.581901:0.209772:0.567387:0.209772:0.000000
2:@0.581900:0.218467:0.587608:0.218467:0.587608:0.208158:0.581900:0.208158:0.000000
Definición:@0.404236:0.249595:0.484320:0.249595:0.484320:0.232649:0.404236:0.232649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.484322:0.249132:0.488464:0.249132:0.488464:0.232635:0.484322:0.232635:0.000000
Sean  ,:@0.404236:0.268247:0.460808:0.269123:0.460808:0.252626:0.404236:0.251749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.506007:0.261088:0.510924:0.261088:0.510924:0.251539:0.506007:0.251539:0.000000
∈:@0.477582:0.269760:0.491318:0.269760:0.491318:0.253479:0.477582:0.253479:0.000000
AB:@0.445755:0.269239:0.473690:0.269239:0.473690:0.252770:0.445755:0.252770:0.000000:0.000000
 con :@0.514070:0.268243:0.549307:0.268243:0.549307:0.251746:0.514070:0.251746:0.000000:0.000000:0.000000:0.000000:0.000000
(,:@0.581502:0.268369:0.605506:0.268369:0.605506:0.251871:0.581502:0.251871:0.000000:0.000000
),:@0.625157:0.268369:0.633518:0.268369:0.633518:0.251871:0.625157:0.251871:0.000000:0.000000
(,:@0.664573:0.268369:0.690216:0.268369:0.690216:0.251871:0.664573:0.251871:0.000000:0.000000
).  Un producto escalar  :@0.711484:0.268369:0.881851:0.268243:0.881851:0.251746:0.711484:0.251871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.595584:0.270588:0.600501:0.270588:0.600501:0.261039:0.595584:0.261039:0.000000
1:@0.619558:0.270588:0.624475:0.270588:0.624475:0.261039:0.619558:0.261039:0.000000
2:@0.679136:0.270588:0.684054:0.270588:0.684054:0.261039:0.679136:0.261039:0.000000
2:@0.704738:0.270588:0.709656:0.270588:0.709656:0.261039:0.704738:0.261039:0.000000
=:@0.567472:0.269005:0.494957:0.269005:0.494957:0.252724:0.567472:0.252724:0.000000
=:@0.650563:0.269005:0.578048:0.269005:0.578048:0.252724:0.650563:0.252724:0.000000
A:@0.553023:0.268485:0.564293:0.268485:0.564293:0.252016:0.553023:0.252016:0.000000
a bB:@0.587469:0.268485:0.646286:0.268485:0.646286:0.252016:0.587469:0.252016:0.000000:0.000000:0.000000:0.000000
ab:@0.670541:0.268485:0.705257:0.268485:0.705257:0.252016:0.670541:0.252016:0.000000:0.000000
de   con   representado por :@0.404228:0.287474:0.628425:0.287480:0.628425:0.270982:0.404228:0.270976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.429953:0.287596:0.441223:0.287596:0.441223:0.271127:0.429953:0.271127:0.000000
B:@0.482465:0.287596:0.491654:0.287596:0.491654:0.271127:0.482465:0.271127:0.000000
⋅:@0.645020:0.288116:0.649836:0.288116:0.649836:0.271835:0.645020:0.271835:0.000000
AB:@0.632151:0.287596:0.660297:0.287596:0.660297:0.271127:0.632151:0.271127:0.000000:0.000000
 está definido como :@0.665279:0.287480:0.811806:0.287480:0.811806:0.270982:0.665279:0.270982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.528571:0.306717:0.531326:0.306717:0.531326:0.290219:0.528571:0.290219:0.000000
12:@0.462922:0.308936:0.481342:0.308936:0.481342:0.299387:0.462922:0.299387:0.000000:0.000000
12:@0.507736:0.308936:0.525901:0.308936:0.525901:0.299387:0.507736:0.299387:0.000000:0.000000
⋅=:@0.420831:0.307353:0.450943:0.307353:0.450943:0.291072:0.420831:0.291072:0.000000:0.000000
+:@0.486160:0.307353:0.496736:0.307353:0.496736:0.291072:0.486160:0.291072:0.000000
AB aa:@0.407943:0.306832:0.476816:0.306832:0.476816:0.290364:0.407943:0.290364:0.000000:0.000000:0.000000:0.000000:0.000000
bb:@0.499453:0.306832:0.521492:0.306832:0.521492:0.290364:0.499453:0.290364:0.000000:0.000000
El número real :@0.404236:0.334339:0.515512:0.334339:0.515512:0.317841:0.404236:0.317841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.534498:0.334975:0.539314:0.334975:0.539314:0.318694:0.534498:0.318694:0.000000
AB:@0.521629:0.334454:0.549775:0.334454:0.549775:0.317985:0.521629:0.317985:0.000000:0.000000
 se llama producto escalar, producto punto o :@0.554758:0.334338:0.895861:0.334338:0.895861:0.317841:0.554758:0.317841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto interior de   con  .:@0.404239:0.353569:0.623848:0.353575:0.623848:0.337077:0.404239:0.337071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.558028:0.353691:0.569298:0.353691:0.569298:0.337222:0.558028:0.337222:0.000000
B:@0.610539:0.353691:0.619728:0.353691:0.619728:0.337222:0.610539:0.337222:0.000000
Nótese que el producto escalar de dos vectores de   es un número :@0.404243:0.378054:0.895895:0.378053:0.895895:0.361556:0.404243:0.361556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.769314:0.377085:0.783223:0.377085:0.783223:0.363638:0.769314:0.363638:0.000000
2:@0.783269:0.371702:0.788222:0.371702:0.788222:0.362084:0.783269:0.362084:0.000000
real.:@0.404226:0.395404:0.432007:0.395404:0.432007:0.378907:0.404226:0.378907:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404226:0.420259:0.534881:0.420259:0.534881:0.403472:0.404226:0.403472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404226:0.446459:0.416498:0.446459:0.416498:0.429744:0.404226:0.429744:0.000000:0.000000
   Sean :@0.416498:0.446242:0.465478:0.446242:0.465478:0.429744:0.416498:0.429744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(3,5),:@0.497684:0.446248:0.532323:0.446248:0.532323:0.429751:0.497684:0.429751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(1,4). Entonces, :@0.563379:0.446248:0.687522:0.446248:0.687522:0.429751:0.563379:0.429751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.483654:0.446884:0.494231:0.446884:0.494231:0.430604:0.483654:0.430604:0.000000
= −:@0.549349:0.446884:0.579929:0.446884:0.579929:0.430604:0.549349:0.430604:0.000000:0.000000:0.000000
A:@0.469212:0.446364:0.480482:0.446364:0.480482:0.429895:0.469212:0.429895:0.000000
B:@0.535908:0.446364:0.545098:0.446364:0.545098:0.429895:0.535908:0.429895:0.000000
3( 1) 54 17.:@0.737676:0.446248:0.875422:0.446248:0.875422:0.429751:0.737676:0.429751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅= ×− +× =:@0.704116:0.446884:0.853171:0.446884:0.853171:0.430604:0.704116:0.430604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.691247:0.446364:0.719393:0.446364:0.719393:0.429895:0.691247:0.429895:0.000000:0.000000
2.:@0.404237:0.472830:0.416509:0.472830:0.416509:0.456115:0.404237:0.456115:0.000000:0.000000
   Sean :@0.416509:0.472613:0.465489:0.472613:0.465489:0.456115:0.416509:0.456115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2,1),:@0.497684:0.472613:0.544538:0.472613:0.544538:0.456115:0.497684:0.456115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(1,2).  Entonces, :@0.575593:0.472613:0.689198:0.472613:0.689198:0.456115:0.575593:0.456115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.483679:0.473249:0.494255:0.473249:0.494255:0.456968:0.483679:0.456968:0.000000
−:@0.517335:0.473249:0.527912:0.473249:0.527912:0.456968:0.517335:0.456968:0.000000
=:@0.561568:0.473249:0.572145:0.473249:0.572145:0.456968:0.561568:0.456968:0.000000
A:@0.469205:0.472728:0.480476:0.472728:0.480476:0.456259:0.469205:0.456259:0.000000
B:@0.548097:0.472728:0.557286:0.472728:0.557286:0.456259:0.548097:0.456259:0.000000
21 (1)2 0.:@0.739351:0.472613:0.867927:0.472613:0.867927:0.456115:0.739351:0.456115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅= ×+ −× =:@0.705772:0.473249:0.852881:0.473249:0.852881:0.456968:0.705772:0.456968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.692903:0.472728:0.721049:0.472728:0.721049:0.456259:0.692903:0.456259:0.000000:0.000000
Demostración.:@0.404238:0.497554:0.517633:0.497554:0.517633:0.480608:0.404238:0.480608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  :@0.404238:0.523450:0.446178:0.523450:0.446178:0.506952:0.404238:0.506952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(, ),:@0.478478:0.523457:0.525273:0.523457:0.525273:0.506959:0.478478:0.506959:0.000000:0.000000:0.000000:0.000000:0.000000
(, ),:@0.556541:0.523457:0.606572:0.523457:0.606572:0.506959:0.556541:0.506959:0.000000:0.000000:0.000000:0.000000:0.000000
(, )  tres elementos de  .:@0.638842:0.523457:0.844691:0.523457:0.844691:0.506959:0.638842:0.506959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.492560:0.525675:0.497477:0.525675:0.497477:0.516127:0.492560:0.516127:0.000000
1:@0.511561:0.525675:0.516478:0.525675:0.516478:0.516127:0.511561:0.516127:0.000000
2:@0.571083:0.525675:0.576001:0.525675:0.576001:0.516127:0.571083:0.516127:0.000000
2:@0.591712:0.525675:0.596630:0.525675:0.596630:0.516127:0.591712:0.516127:0.000000
3:@0.653383:0.525675:0.658300:0.525675:0.658300:0.516127:0.653383:0.516127:0.000000
3:@0.673800:0.525675:0.678717:0.525675:0.678717:0.516127:0.673800:0.516127:0.000000
=:@0.464394:0.524093:0.396908:0.524093:0.396908:0.507812:0.464394:0.507812:0.000000
=:@0.542457:0.524093:0.474971:0.524093:0.474971:0.507812:0.542457:0.507812:0.000000
=:@0.624739:0.524093:0.635315:0.524093:0.635315:0.507812:0.624739:0.507812:0.000000
A:@0.449887:0.523572:0.461157:0.523572:0.461157:0.507103:0.449887:0.507103:0.000000
a bB:@0.484449:0.523572:0.538141:0.523572:0.538141:0.507103:0.484449:0.507103:0.000000:0.000000:0.000000:0.000000
ab C:@0.562493:0.523572:0.620269:0.523572:0.620269:0.507103:0.562493:0.507103:0.000000:0.000000:0.000000:0.000000
a b:@0.644794:0.523572:0.674308:0.523572:0.674308:0.507103:0.644794:0.507103:0.000000:0.000000:0.000000
R:@0.823073:0.522488:0.836983:0.522488:0.836983:0.509041:0.823073:0.509041:0.000000
2:@0.836982:0.517104:0.841936:0.517104:0.841936:0.507485:0.836982:0.507485:0.000000
i):@0.404229:0.548152:0.414768:0.548152:0.414768:0.531438:0.404229:0.531438:0.000000:0.000000
   De la definición de producto escalar, se tiene :@0.414768:0.547936:0.749573:0.547936:0.749573:0.531438:0.414768:0.531438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.688921:0.567172:0.691676:0.567172:0.691676:0.550674:0.688921:0.550674:0.000000
12:@0.486480:0.569391:0.504645:0.569391:0.504645:0.559842:0.486480:0.559842:0.000000:0.000000
12:@0.530771:0.569391:0.548668:0.569391:0.548668:0.559842:0.530771:0.559842:0.000000:0.000000
21:@0.577102:0.569391:0.595947:0.569391:0.595947:0.559842:0.577102:0.559842:0.000000:0.000000
21:@0.621393:0.569391:0.639970:0.569391:0.639970:0.559842:0.621393:0.559842:0.000000:0.000000
⋅=:@0.444284:0.567808:0.474435:0.567808:0.474435:0.551527:0.444284:0.551527:0.000000:0.000000
+:@0.509208:0.567808:0.519785:0.567808:0.519785:0.551527:0.509208:0.551527:0.000000
=:@0.554019:0.567808:0.564596:0.567808:0.564596:0.551527:0.554019:0.551527:0.000000
+:@0.599351:0.567808:0.609927:0.567808:0.609927:0.551527:0.599351:0.551527:0.000000
= ⋅:@0.644161:0.567808:0.674947:0.567808:0.674947:0.551527:0.644161:0.551527:0.000000:0.000000:0.000000
AB aa:@0.431415:0.567287:0.500134:0.567287:0.500134:0.550819:0.431415:0.550819:0.000000:0.000000:0.000000:0.000000:0.000000
bb:@0.522521:0.567287:0.544310:0.567287:0.544310:0.550819:0.522521:0.550819:0.000000:0.000000
aa:@0.568545:0.567287:0.591914:0.567287:0.591914:0.550819:0.568545:0.550819:0.000000:0.000000
bb:@0.612682:0.567287:0.636089:0.567287:0.636089:0.550819:0.612682:0.550819:0.000000:0.000000
BA:@0.658244:0.567287:0.688626:0.567287:0.688626:0.550819:0.658244:0.550819:0.000000:0.000000
ii):@0.404236:0.593753:0.419032:0.593753:0.419032:0.577038:0.404236:0.577038:0.000000:0.000000:0.000000
   En primer lugar, :@0.419032:0.593536:0.542753:0.593536:0.542753:0.577038:0.419032:0.577038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(, )( ,) (:@0.601079:0.593536:0.737477:0.593536:0.737477:0.577038:0.601079:0.577038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.784291:0.593536:0.787046:0.593536:0.787046:0.577038:0.784291:0.577038:0.000000
).   :@0.835864:0.593536:0.855938:0.593536:0.855938:0.577038:0.835864:0.577038:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.615161:0.595755:0.620078:0.595755:0.620078:0.586206:0.615161:0.586206:0.000000
1:@0.636782:0.595755:0.641699:0.595755:0.641699:0.586206:0.636782:0.586206:0.000000
2:@0.678452:0.595755:0.683370:0.595755:0.683370:0.586206:0.678452:0.586206:0.000000
2:@0.701701:0.595755:0.706619:0.595755:0.706619:0.586206:0.701701:0.586206:0.000000
1:@0.745613:0.595755:0.750531:0.595755:0.750531:0.586206:0.745613:0.586206:0.000000
2:@0.776244:0.595755:0.781161:0.595755:0.781161:0.586206:0.776244:0.586206:0.000000
1:@0.799014:0.595755:0.803931:0.595755:0.803931:0.586206:0.799014:0.586206:0.000000
2:@0.829377:0.595755:0.834295:0.595755:0.834295:0.586206:0.829377:0.586206:0.000000
+=:@0.560193:0.594172:0.597567:0.594172:0.597567:0.577891:0.560193:0.577891:0.000000:0.000000
+:@0.650604:0.594172:0.661181:0.594172:0.661181:0.577891:0.650604:0.577891:0.000000
=:@0.717455:0.594172:0.728032:0.594172:0.728032:0.577891:0.717455:0.577891:0.000000
+:@0.753944:0.594172:0.764521:0.594172:0.764521:0.577891:0.753944:0.577891:0.000000
+:@0.807347:0.594172:0.817924:0.594172:0.817924:0.577891:0.807347:0.577891:0.000000
AB:@0.546476:0.593652:0.582675:0.593652:0.582675:0.577183:0.546476:0.577183:0.000000:0.000000
ab:@0.607046:0.593652:0.637774:0.593652:0.637774:0.577183:0.607046:0.577183:0.000000:0.000000
ab:@0.669870:0.593652:0.702216:0.593652:0.702216:0.577183:0.669870:0.577183:0.000000:0.000000
a:@0.737510:0.593652:0.746488:0.593652:0.746488:0.577183:0.737510:0.577183:0.000000
a b:@0.767660:0.593652:0.800014:0.593652:0.800014:0.577183:0.767660:0.577183:0.000000:0.000000:0.000000
b:@0.820647:0.593652:0.829914:0.593652:0.829914:0.577183:0.820647:0.577183:0.000000
 :@0.404245:0.618015:0.408387:0.618015:0.408387:0.601517:0.404245:0.601517:0.000000
  Luego, por la definición del producto escalar en :@0.427698:0.618015:0.781433:0.618015:0.781433:0.601517:0.427698:0.601517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.783109:0.617046:0.797019:0.617046:0.797019:0.603599:0.783109:0.603599:0.000000
2:@0.796989:0.611663:0.801943:0.611663:0.801943:0.602044:0.796989:0.602044:0.000000
, obtenemos  :@0.801941:0.618016:0.895914:0.618016:0.895914:0.601518:0.801941:0.601518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.552389:0.637252:0.555144:0.637252:0.555144:0.620755:0.552389:0.620755:0.000000
,  entonces :@0.684202:0.637252:0.763696:0.638510:0.763696:0.622012:0.684202:0.620755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
13:@0.487474:0.639471:0.505638:0.639471:0.505638:0.629922:0.487474:0.629922:0.000000:0.000000
13:@0.531553:0.639471:0.549450:0.639471:0.549450:0.629922:0.531553:0.629922:0.000000:0.000000
23:@0.616521:0.639471:0.635834:0.639471:0.635834:0.629922:0.616521:0.629922:0.000000:0.000000
23:@0.662223:0.639471:0.681280:0.639471:0.681280:0.629922:0.662223:0.629922:0.000000:0.000000
⋅=:@0.444284:0.637889:0.475436:0.637889:0.475436:0.621608:0.444284:0.621608:0.000000:0.000000
+:@0.509979:0.637889:0.520556:0.637889:0.520556:0.621608:0.509979:0.621608:0.000000
⋅ =:@0.572861:0.637889:0.604013:0.637889:0.604013:0.621608:0.572861:0.621608:0.000000:0.000000:0.000000
+:@0.640193:0.637889:0.650769:0.637889:0.650769:0.621608:0.640193:0.621608:0.000000
AC aa:@0.431415:0.637368:0.501117:0.637368:0.501117:0.620899:0.431415:0.620899:0.000000:0.000000:0.000000:0.000000:0.000000
bb BC aa:@0.523291:0.637368:0.631312:0.637368:0.631312:0.620899:0.523291:0.620899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bb:@0.653486:0.637368:0.676893:0.637368:0.676893:0.620899:0.653486:0.620899:0.000000:0.000000
 :@0.404227:0.665288:0.408369:0.665288:0.408369:0.648790:0.404227:0.648790:0.000000
(:@0.430254:0.657746:0.436207:0.657746:0.436207:0.641249:0.430254:0.641249:0.000000
):@0.473697:0.657746:0.479650:0.657746:0.479650:0.641249:0.473697:0.641249:0.000000
(:@0.516004:0.657746:0.521957:0.657746:0.521957:0.641249:0.516004:0.641249:0.000000
):@0.567211:0.657746:0.573164:0.657746:0.573164:0.641249:0.567211:0.641249:0.000000
(:@0.604682:0.657746:0.610635:0.657746:0.610635:0.641249:0.604682:0.641249:0.000000
):@0.655350:0.657746:0.661303:0.657746:0.661303:0.641249:0.655350:0.641249:0.000000
1:@0.530089:0.659965:0.535006:0.659965:0.535006:0.650416:0.530089:0.650416:0.000000
2:@0.560720:0.659965:0.565637:0.659965:0.565637:0.650416:0.560720:0.650416:0.000000
3:@0.582129:0.659965:0.587047:0.659965:0.587047:0.650416:0.582129:0.650416:0.000000
1:@0.618514:0.659965:0.623431:0.659965:0.623431:0.650416:0.618514:0.650416:0.000000
2:@0.648877:0.659965:0.653795:0.659965:0.653795:0.650416:0.648877:0.650416:0.000000
3:@0.670030:0.659965:0.674948:0.659965:0.674948:0.650416:0.670030:0.650416:0.000000
13:@0.702691:0.659965:0.720855:0.659965:0.720855:0.650416:0.702691:0.650416:0.000000:0.000000
23:@0.747506:0.659965:0.766819:0.659965:0.766819:0.650416:0.747506:0.650416:0.000000:0.000000
13:@0.795097:0.659965:0.814466:0.659965:0.814466:0.650416:0.795097:0.650416:0.000000:0.000000
23:@0.840846:0.659965:0.859902:0.659965:0.859902:0.650416:0.840846:0.650416:0.000000:0.000000
+:@0.450672:0.658383:0.461249:0.658383:0.461249:0.642102:0.450672:0.642102:0.000000
⋅ =:@0.481342:0.658383:0.512494:0.658383:0.512494:0.642102:0.481342:0.642102:0.000000:0.000000:0.000000
+:@0.538406:0.658383:0.548983:0.658383:0.548983:0.642102:0.538406:0.642102:0.000000
+:@0.591386:0.658383:0.601962:0.658383:0.601962:0.642102:0.591386:0.642102:0.000000
+:@0.626834:0.658383:0.637410:0.658383:0.637410:0.642102:0.626834:0.642102:0.000000
=:@0.680064:0.658383:0.690640:0.658383:0.690640:0.642102:0.680064:0.642102:0.000000
+:@0.725183:0.658383:0.735759:0.658383:0.735759:0.642102:0.725183:0.642102:0.000000
+:@0.771166:0.658383:0.781742:0.658383:0.781742:0.642102:0.771166:0.642102:0.000000
+:@0.818809:0.658383:0.829385:0.658383:0.829385:0.642102:0.818809:0.642102:0.000000
AB C:@0.436955:0.657862:0.497467:0.657862:0.497467:0.641393:0.436955:0.641393:0.000000:0.000000:0.000000:0.000000
a:@0.521992:0.657862:0.530970:0.657862:0.530970:0.641393:0.521992:0.641393:0.000000
aa:@0.552142:0.657862:0.582524:0.657862:0.582524:0.641393:0.552142:0.641393:0.000000:0.000000
b:@0.610246:0.657862:0.619513:0.657862:0.619513:0.641393:0.610246:0.641393:0.000000
b b:@0.640146:0.657862:0.670547:0.657862:0.670547:0.641393:0.640146:0.641393:0.000000:0.000000:0.000000
a a:@0.694570:0.657862:0.716321:0.657862:0.716321:0.641393:0.694570:0.641393:0.000000:0.000000:0.000000
a a:@0.738919:0.657862:0.762288:0.657862:0.762288:0.641393:0.738919:0.641393:0.000000:0.000000:0.000000
b b:@0.784462:0.657862:0.810064:0.657862:0.810064:0.641393:0.784462:0.641393:0.000000:0.000000:0.000000
b b:@0.832103:0.657862:0.855505:0.657862:0.855505:0.641393:0.832103:0.641393:0.000000:0.000000:0.000000
 :@0.404237:0.692071:0.408379:0.692071:0.408379:0.675573:0.404237:0.675573:0.000000
.:@0.702534:0.684527:0.705289:0.684527:0.705289:0.668029:0.702534:0.668029:0.000000
13:@0.453289:0.686746:0.471453:0.686746:0.471453:0.677197:0.453289:0.677197:0.000000:0.000000
13:@0.497368:0.686746:0.515265:0.686746:0.515265:0.677197:0.497368:0.677197:0.000000:0.000000
23:@0.541915:0.686746:0.561228:0.686746:0.561228:0.677197:0.541915:0.677197:0.000000:0.000000
23:@0.587622:0.686746:0.606678:0.686746:0.606678:0.677197:0.587622:0.677197:0.000000:0.000000
=:@0.430673:0.685163:0.441250:0.685163:0.441250:0.668882:0.430673:0.668882:0.000000
+:@0.475792:0.685163:0.486369:0.685163:0.486369:0.668882:0.475792:0.668882:0.000000
+:@0.519621:0.685163:0.530197:0.685163:0.530197:0.668882:0.519621:0.668882:0.000000
+:@0.565588:0.685163:0.576164:0.685163:0.576164:0.668882:0.565588:0.668882:0.000000
=⋅ +⋅:@0.611805:0.685163:0.689695:0.685163:0.689695:0.668882:0.611805:0.668882:0.000000:0.000000:0.000000:0.000000:0.000000
aa:@0.445161:0.684643:0.466911:0.684643:0.466911:0.668174:0.445161:0.668174:0.000000:0.000000
bb:@0.489085:0.684643:0.510874:0.684643:0.510874:0.668174:0.489085:0.668174:0.000000:0.000000
aa:@0.533318:0.684643:0.556687:0.684643:0.556687:0.668174:0.533318:0.668174:0.000000:0.000000
bb:@0.578861:0.684643:0.602269:0.684643:0.602269:0.668174:0.578861:0.668174:0.000000:0.000000
AC BC:@0.627025:0.684643:0.701001:0.684643:0.701001:0.668174:0.627025:0.668174:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.718322:0.408378:0.718322:0.408378:0.701824:0.404236:0.701824:0.000000
Después, (+ )=:@0.427682:0.718322:0.570041:0.718435:0.570041:0.701937:0.427682:0.701824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.599330:0.718435:0.610137:0.718435:0.610137:0.701937:0.599330:0.701937:0.000000
.  :@0.639266:0.718435:0.650223:0.718322:0.650223:0.701825:0.639266:0.701937:0.000000:0.000000:0.000000
⋅:@0.542006:0.719071:0.506308:0.719071:0.506308:0.702790:0.542006:0.702790:0.000000
⋅:@0.582521:0.719071:0.546823:0.719071:0.546823:0.702790:0.582521:0.702790:0.000000
⋅:@0.621630:0.719071:0.626446:0.719071:0.626446:0.702790:0.621630:0.702790:0.000000
AB CA CB C:@0.503476:0.718551:0.637735:0.718551:0.637735:0.702082:0.503476:0.702082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las otras propiedades se proponen como ejercicios para el estudiante.:@0.404244:0.742801:0.891807:0.742801:0.891807:0.726304:0.404244:0.726304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición de subespacio vectorial:@0.404236:0.779655:0.679157:0.779655:0.679157:0.761972:0.404236:0.761972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un subconjunto V de :@0.404236:0.803490:0.569935:0.803490:0.569935:0.786992:0.404236:0.786992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.572343:0.802521:0.586252:0.802521:0.586252:0.789075:0.572343:0.789075:0.000000
2:@0.586243:0.797137:0.591196:0.797137:0.591196:0.787519:0.586243:0.787519:0.000000
 es un subespacio vectorial de :@0.591196:0.803490:0.819122:0.803490:0.819122:0.786992:0.591196:0.786992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.821530:0.802521:0.835439:0.802521:0.835439:0.789075:0.821530:0.789075:0.000000
2:@0.835423:0.797137:0.840376:0.797137:0.840376:0.787519:0.835423:0.787519:0.000000
 si este :@0.840376:0.803490:0.895916:0.803490:0.895916:0.786992:0.840376:0.786992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con las mismas operaciones de adición \+\ y producto de escalares :@0.404230:0.820841:0.895895:0.820841:0.895895:0.804343:0.404230:0.804343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por elementos de :@0.404230:0.838192:0.537640:0.838192:0.537640:0.821694:0.404230:0.821694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.539663:0.837223:0.553573:0.837223:0.553573:0.823776:0.539663:0.823776:0.000000
2:@0.553589:0.831840:0.558542:0.831840:0.558542:0.822222:0.553589:0.822222:0.000000
, satisface las mismas propiedades del espacio :@0.558543:0.838192:0.895891:0.838192:0.895891:0.821694:0.558543:0.821694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectorial  .:@0.404228:0.855542:0.490912:0.855542:0.490912:0.839045:0.404228:0.839045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.469287:0.854574:0.483196:0.854574:0.483196:0.841127:0.469287:0.841127:0.000000
2:@0.483204:0.849191:0.488157:0.849191:0.488157:0.839573:0.483204:0.839573:0.000000
Ejemplo::@0.404238:0.880021:0.465153:0.880021:0.465153:0.863524:0.404238:0.863524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V :@0.404238:0.904616:0.419130:0.904616:0.419130:0.888147:0.404238:0.888147:0.000000:0.000000
= { (:@0.420960:0.904500:0.455214:0.904500:0.455214:0.888003:0.420960:0.888003:0.000000:0.000000:0.000000:0.000000:0.000000
t a, b t:@0.443597:0.904616:0.498618:0.904616:0.498618:0.888147:0.443597:0.888147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)|  :@0.481992:0.904500:0.502760:0.904500:0.502760:0.888003:0.481992:0.888003:0.000000:0.000000:0.000000:0.000000
 :@0.504591:0.904284:0.525455:0.904284:0.525455:0.889637:0.504591:0.889637:0.000000:0.000000
R:@0.527593:0.903532:0.541503:0.903532:0.541503:0.890085:0.527593:0.890085:0.000000
}, donde (a, b) :@0.541503:0.904500:0.651486:0.904500:0.651486:0.888003:0.541503:0.888003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.653317:0.904284:0.674181:0.904284:0.674181:0.889637:0.653317:0.889637:0.000000:0.000000
R:@0.676340:0.903532:0.690250:0.903532:0.690250:0.890085:0.676340:0.890085:0.000000
2:@0.690247:0.898147:0.695200:0.898147:0.695200:0.888529:0.690247:0.888529:0.000000
 no nulo, es un subespacio :@0.695199:0.904500:0.895883:0.904500:0.895883:0.888003:0.695199:0.888003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vectorial de  .:@0.404235:0.921851:0.512911:0.921851:0.512911:0.905353:0.404235:0.905354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.491295:0.920882:0.505205:0.920882:0.505205:0.907436:0.491295:0.907436:0.000000
2:@0.505205:0.915498:0.510158:0.915498:0.510158:0.905880:0.505205:0.905880:0.000000
El producto escalar en :@0.199880:0.417871:0.347600:0.417871:0.347600:0.402808:0.199880:0.402808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.153337:0.432828:0.166037:0.432828:0.166037:0.420551:0.153337:0.420551:0.000000
2:@0.166044:0.427914:0.170566:0.427914:0.170566:0.419132:0.166044:0.419132:0.000000
 que hemos definido es el :@0.170565:0.433713:0.340411:0.433713:0.340411:0.418650:0.170565:0.418650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más utilizado. Cabe precisar :@0.153345:0.449555:0.337159:0.449555:0.337159:0.434492:0.153345:0.434492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que un producto escalar en   :@0.153345:0.465397:0.357017:0.465397:0.357017:0.450334:0.153345:0.450334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.336014:0.464512:0.348714:0.464512:0.348714:0.452235:0.336014:0.452235:0.000000
2:@0.348714:0.459598:0.353236:0.459598:0.353236:0.450816:0.348714:0.450816:0.000000
es una función:@0.153342:0.481239:0.248837:0.481239:0.248837:0.466176:0.153342:0.466176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.187366:0.531211:0.215470:0.531211:0.215470:0.514946:0.187366:0.514946:0.000000:0.000000
AB:@0.248026:0.531211:0.275406:0.531211:0.275406:0.514946:0.248026:0.514946:0.000000:0.000000
•::@0.155895:0.518601:0.167140:0.518601:0.167140:0.502308:0.155895:0.502308:0.000000:0.000000
,:@0.280600:0.508205:0.283321:0.508205:0.283321:0.491911:0.280600:0.491911:0.000000
(, ):@0.180764:0.531097:0.221889:0.531097:0.221889:0.514803:0.180764:0.514803:0.000000:0.000000:0.000000:0.000000
,:@0.277487:0.531097:0.280208:0.531097:0.280208:0.514803:0.277487:0.514803:0.000000
2:@0.195691:0.500265:0.200547:0.500265:0.200547:0.490834:0.195691:0.490834:0.000000
2:@0.232871:0.500265:0.237728:0.500265:0.237728:0.490834:0.232871:0.490834:0.000000
×:@0.204997:0.508830:0.215443:0.508830:0.215443:0.492750:0.204997:0.492750:0.000000
→:@0.242899:0.508830:0.261679:0.508830:0.261679:0.492750:0.242899:0.492750:0.000000
→⋅:@0.224903:0.531725:0.265280:0.531725:0.265280:0.515645:0.224903:0.515645:0.000000:0.000000
y satisface las propiedades simi-:@0.153344:0.554628:0.357666:0.554628:0.357666:0.539564:0.153344:0.539564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lares desde el literal  hasta el :@0.153344:0.570470:0.344421:0.570470:0.344421:0.555406:0.153344:0.555406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i. :@0.281749:0.570575:0.291633:0.570575:0.291633:0.555538:0.281749:0.555538:0.000000:0.000000:0.000000
iv. :@0.344421:0.570575:0.360181:0.570575:0.360181:0.555538:0.344421:0.555538:0.000000:0.000000:0.000000:0.000000
del teorema precedente.:@0.153344:0.586312:0.311285:0.586312:0.311285:0.571248:0.153344:0.571248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.155542:0.619562:0.222487:0.619562:0.222487:0.602616:0.155542:0.602616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,,:@0.155542:0.645458:0.229866:0.645465:0.229866:0.628967:0.155542:0.628960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.288503:0.646101:0.300659:0.646101:0.305432:0.629820:0.293276:0.629820:0.000000
∈:@0.247628:0.646101:0.261364:0.646101:0.261364:0.629820:0.247628:0.629820:0.000000
∈:@0.307042:0.646101:0.320778:0.646101:0.320778:0.629820:0.307042:0.629820:0.000000
AB C:@0.197058:0.645581:0.243583:0.645581:0.243583:0.629112:0.197058:0.629112:0.000000:0.000000:0.000000:0.000000
,:@0.284117:0.645465:0.286872:0.645465:0.286872:0.628967:0.284117:0.628967:0.000000
2:@0.276055:0.637428:0.280973:0.637428:0.280973:0.627879:0.276055:0.627879:0.000000
.  :@0.334829:0.645465:0.345868:0.645465:0.345868:0.628967:0.334829:0.628967:0.000000:0.000000:0.000000
El producto escalar en   :@0.155547:0.662816:0.340333:0.662816:0.340333:0.646318:0.155547:0.646318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.317335:0.661847:0.331244:0.661847:0.331244:0.648400:0.317335:0.648400:0.000000
2:@0.331238:0.656463:0.336191:0.656463:0.336191:0.646845:0.331238:0.646845:0.000000
arriba definido satisface las :@0.155541:0.680167:0.348960:0.680167:0.348960:0.663669:0.155541:0.663669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades siguientes: :@0.155541:0.697517:0.324551:0.697517:0.324551:0.681020:0.155541:0.681020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.155541:0.724093:0.166079:0.724093:0.166079:0.707378:0.155541:0.707378:0.000000:0.000000
 :@0.166079:0.723876:0.170221:0.723876:0.170221:0.707378:0.166079:0.707378:0.000000
=:@0.211820:0.723882:0.222628:0.723882:0.222628:0.707384:0.211820:0.707384:0.000000
.:@0.252913:0.723882:0.255668:0.723882:0.255668:0.707384:0.252913:0.707384:0.000000
⋅:@0.195598:0.724518:0.161884:0.724518:0.161884:0.708237:0.195598:0.708237:0.000000
⋅:@0.234129:0.724518:0.200415:0.724518:0.200415:0.708237:0.234129:0.708237:0.000000
AB BA:@0.182729:0.723997:0.252643:0.723997:0.252643:0.707529:0.182729:0.707529:0.000000:0.000000:0.000000:0.000000:0.000000
ii):@0.155542:0.750463:0.170338:0.750463:0.170338:0.733748:0.155542:0.733748:0.000000:0.000000:0.000000
  (:@0.170338:0.750246:0.187513:0.750246:0.187513:0.733748:0.170338:0.733748:0.000000:0.000000:0.000000
):@0.225003:0.750246:0.230956:0.750246:0.230956:0.733748:0.225003:0.733748:0.000000
.:@0.343850:0.750246:0.346605:0.750246:0.346605:0.733748:0.343850:0.733748:0.000000
+:@0.201981:0.750882:0.212558:0.750882:0.212558:0.734601:0.201981:0.734601:0.000000
⋅ =⋅ +⋅:@0.232651:0.750882:0.331039:0.750882:0.331039:0.734601:0.232651:0.734601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB C:@0.188284:0.750362:0.248796:0.750362:0.248796:0.733893:0.188284:0.733893:0.000000:0.000000:0.000000:0.000000
A CB C:@0.268388:0.750362:0.342348:0.750362:0.342348:0.733893:0.268388:0.733893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii):@0.155541:0.778085:0.174595:0.778085:0.174595:0.761370:0.155541:0.761370:0.000000:0.000000:0.000000:0.000000
  (:@0.174595:0.777868:0.187513:0.776610:0.187513:0.760113:0.174595:0.761370:0.000000:0.000000:0.000000
) =(:@0.211672:0.776610:0.266250:0.776610:0.266250:0.760113:0.211672:0.760113:0.000000:0.000000:0.000000:0.000000
).:@0.294589:0.776610:0.302950:0.776610:0.302950:0.760113:0.294589:0.760113:0.000000:0.000000
α:@0.185057:0.777246:0.197213:0.777246:0.201986:0.760966:0.189829:0.760966:0.000000
α:@0.244683:0.777246:0.256839:0.777246:0.261612:0.760966:0.249455:0.760966:0.000000
⋅:@0.219306:0.777246:0.224123:0.777246:0.224123:0.760966:0.219306:0.760966:0.000000
⋅:@0.278778:0.777246:0.283595:0.777246:0.283595:0.760966:0.278778:0.760966:0.000000
AB:@0.200931:0.776726:0.234568:0.776726:0.234568:0.760257:0.200931:0.760257:0.000000:0.000000
AB:@0.265893:0.776726:0.294040:0.776726:0.294040:0.760257:0.265893:0.760257:0.000000:0.000000
iv):@0.155542:0.814319:0.174345:0.814319:0.174345:0.797605:0.155542:0.797605:0.000000:0.000000:0.000000
 :@0.174345:0.814102:0.178487:0.814102:0.178487:0.797605:0.174345:0.797605:0.000000
⋅:@0.203898:0.806987:0.208773:0.806987:0.208773:0.790505:0.203898:0.790505:0.000000
⋅:@0.203898:0.830455:0.208773:0.830455:0.208773:0.813973:0.203898:0.813973:0.000000
≠:@0.283919:0.830455:0.294626:0.830455:0.294626:0.813973:0.283919:0.813973:0.000000
AA:@0.190859:0.806460:0.222630:0.806460:0.222630:0.789788:0.190859:0.789788:0.000000:0.000000
A:@0.270042:0.806460:0.281451:0.806460:0.281451:0.789788:0.270042:0.789788:0.000000
AA:@0.190859:0.829928:0.222630:0.829928:0.222630:0.813256:0.190859:0.813256:0.000000:0.000000
A:@0.269242:0.829928:0.280652:0.829928:0.280652:0.813256:0.269242:0.813256:0.000000
=0:@0.222499:0.806343:0.241651:0.806343:0.241651:0.789642:0.222499:0.789642:0.000000:0.000000
=0,:@0.281321:0.806343:0.305407:0.806343:0.305407:0.789642:0.281321:0.789642:0.000000:0.000000:0.000000
>0:@0.221704:0.829811:0.240856:0.829811:0.240856:0.813109:0.221704:0.813109:0.000000:0.000000
0.:@0.298761:0.829811:0.310072:0.829811:0.310072:0.813109:0.298761:0.813109:0.000000:0.000000
Competencia :@0.199644:0.381393:0.297267:0.381393:0.297267:0.365920:0.199644:0.365920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.393961:0.283707:0.393961:0.283707:0.378488:0.199644:0.378488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000