71:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 7. Con las matrices::@0.073089:0.135942:0.230302:0.135942:0.230302:0.119273:0.073089:0.119273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A = , B = , C = :@0.073089:0.180181:0.331945:0.180181:0.331945:0.165266:0.073089:0.165266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.332363:0.180181:0.389242:0.180181:0.389242:0.165241:0.332363:0.165241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Determina:@0.111025:0.221155:0.187463:0.221155:0.187463:0.205749:0.111025:0.205749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la matriz X que se define en cada caso.:@0.187381:0.221155:0.444065:0.221155:0.444065:0.206215:0.187381:0.206215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8. Dadas las matrices, encuentra el producto matricial :@0.073089:0.337944:0.489477:0.337944:0.489477:0.321274:0.073089:0.321274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de cada literal.:@0.103214:0.354586:0.212505:0.354586:0.212505:0.337916:0.103214:0.337916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073100:0.408464:0.104834:0.408464:0.104834:0.392030:0.073100:0.392030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A = :@0.104705:0.388896:0.131966:0.388896:0.131966:0.372490:0.104705:0.372490:0.000000:0.000000:0.000000:0.000000 7:@0.137905:0.380077:0.150919:0.380077:0.150919:0.363643:0.137905:0.363643:0.000000:0.000000 1:@0.170228:0.380077:0.187273:0.380077:0.187273:0.363643:0.170228:0.363643:0.000000:0.000000:0.000000 –8 9 :@0.137905:0.398674:0.191304:0.398674:0.191304:0.382240:0.137905:0.382240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B = :@0.197526:0.388897:0.230217:0.388897:0.230217:0.372491:0.197526:0.372491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.236166:0.380077:0.249180:0.380077:0.249180:0.363643:0.236166:0.363643:0.000000:0.000000 0:@0.268489:0.380077:0.285534:0.380077:0.285534:0.363643:0.268489:0.363643:0.000000:0.000000:0.000000 –3 12 :@0.236166:0.398674:0.294057:0.398674:0.294057:0.382240:0.236166:0.382240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C = :@0.295787:0.388897:0.329546:0.388897:0.329546:0.372491:0.295787:0.372491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.335493:0.380077:0.348507:0.380077:0.348507:0.363643:0.335493:0.363643:0.000000:0.000000 0:@0.367816:0.380077:0.384861:0.380077:0.384861:0.363643:0.367816:0.363643:0.000000:0.000000:0.000000 –3 4 :@0.335493:0.398674:0.390899:0.398674:0.390899:0.382240:0.335493:0.382240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. A B:@0.104633:0.439401:0.167231:0.439401:0.167231:0.422967:0.104633:0.422967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅:@0.149468:0.438985:0.154070:0.438985:0.154070:0.421997:0.149468:0.421997:0.000000 b. A C :@0.104633:0.481060:0.172458:0.481060:0.172458:0.464626:0.104633:0.464626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅:@0.149468:0.480644:0.154070:0.480644:0.154070:0.463655:0.149468:0.463655:0.000000 c. C B:@0.104633:0.519944:0.166955:0.519944:0.166955:0.503510:0.104633:0.503510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅:@0.149192:0.519528:0.153793:0.519528:0.153793:0.502539:0.149192:0.502539:0.000000 9. Dadas las matrices A y B, encuentra la matriz X tal :@0.073089:0.567523:0.489930:0.567523:0.489930:0.550854:0.073089:0.550854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que A – 2X = 3B.:@0.103214:0.584165:0.225729:0.584165:0.225729:0.567495:0.103214:0.567495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.116437:0.623619:0.126759:0.623619:0.126759:0.605161:0.116437:0.605161:0.000000 ⎛:@0.130106:0.612910:0.137326:0.612910:0.137326:0.594452:0.130106:0.594452:0.000000 ⎝:@0.130106:0.635560:0.137326:0.635560:0.137326:0.617103:0.130106:0.617103:0.000000 ⎜:@0.130106:0.628676:0.137326:0.628676:0.137326:0.610218:0.130106:0.610218:0.000000 ⎞:@0.195386:0.612896:0.202606:0.612896:0.202606:0.594438:0.195386:0.594438:0.000000 ⎠:@0.195386:0.635546:0.202606:0.635546:0.202606:0.617089:0.195386:0.617089:0.000000 ⎟:@0.195386:0.628662:0.202606:0.628662:0.202606:0.610204:0.195386:0.610204:0.000000 =:@0.251039:0.623590:0.261361:0.623590:0.261361:0.605133:0.251039:0.605133:0.000000 −:@0.284638:0.615899:0.294960:0.615899:0.294960:0.597441:0.284638:0.597441:0.000000 ⎛:@0.264708:0.612881:0.271928:0.612881:0.271928:0.594424:0.264708:0.594424:0.000000 ⎝:@0.264708:0.635532:0.271928:0.635532:0.271928:0.617074:0.264708:0.617074:0.000000 ⎜:@0.264708:0.628648:0.271928:0.628648:0.271928:0.610190:0.264708:0.610190:0.000000 ⎞:@0.342059:0.612867:0.349279:0.612867:0.349279:0.594410:0.342059:0.594410:0.000000 ⎠:@0.342059:0.635518:0.349279:0.635518:0.349279:0.617060:0.342059:0.617060:0.000000 ⎟:@0.342059:0.628633:0.349279:0.628633:0.349279:0.610176:0.342059:0.610176:0.000000 A:@0.103561:0.623007:0.113658:0.623007:0.113658:0.606249:0.103561:0.606249:0.000000 B:@0.238164:0.623007:0.247189:0.623007:0.247189:0.606249:0.238164:0.606249:0.000000 35:@0.149659:0.615322:0.185213:0.615322:0.185213:0.598536:0.149659:0.598536:0.000000:0.000000 16:@0.150241:0.633708:0.185006:0.633708:0.185006:0.616922:0.150241:0.616922:0.000000:0.000000 y:@0.217326:0.622999:0.225599:0.622999:0.225599:0.606213:0.217326:0.606213:0.000000 6 2:@0.294771:0.615307:0.331294:0.615307:0.331294:0.598521:0.294771:0.598521:0.000000:0.000000:0.000000 3:@0.289925:0.633712:0.299100:0.633712:0.299100:0.616926:0.289925:0.616926:0.000000 4:@0.322133:0.633712:0.331308:0.633712:0.331308:0.616926:0.322133:0.616926:0.000000 –2:@0.337551:0.168529:0.354018:0.168529:0.354018:0.153589:0.337551:0.153589:0.000000:0.000000 0:@0.375179:0.168529:0.383345:0.168529:0.383345:0.153589:0.375179:0.153589:0.000000 4:@0.341695:0.189974:0.349861:0.189974:0.349861:0.175034:0.341695:0.175034:0.000000 –5:@0.371029:0.189974:0.387495:0.189974:0.387495:0.175034:0.371029:0.175034:0.000000:0.000000 0:@0.241864:0.168529:0.250030:0.168529:0.250030:0.153589:0.241864:0.153589:0.000000 2:@0.272972:0.168529:0.281138:0.168529:0.281138:0.153589:0.272972:0.153589:0.000000 –2:@0.237714:0.189974:0.254180:0.189974:0.254180:0.175034:0.237714:0.175034:0.000000:0.000000 1:@0.272972:0.189974:0.281138:0.189974:0.281138:0.175034:0.272972:0.175034:0.000000 3:@0.150104:0.170107:0.158270:0.170107:0.158270:0.155167:0.150104:0.155167:0.000000 1:@0.150104:0.196911:0.158270:0.196911:0.158270:0.181971:0.150104:0.181971:0.000000 0:@0.176476:0.196911:0.184642:0.196911:0.184642:0.181971:0.176476:0.181971:0.000000 1:@0.176531:0.160924:0.184698:0.160924:0.184698:0.145984:0.176531:0.145984:0.000000 2:@0.176531:0.177314:0.184698:0.177314:0.184698:0.162374:0.176531:0.162374:0.000000 1:@0.192454:0.246183:0.200620:0.246183:0.200620:0.231243:0.192454:0.231243:0.000000 2:@0.192454:0.262573:0.200620:0.262573:0.200620:0.247633:0.192454:0.247633:0.000000 1:@0.238609:0.246183:0.246775:0.246183:0.246775:0.231243:0.238609:0.231243:0.000000 3:@0.238609:0.262573:0.246775:0.262573:0.246775:0.247633:0.238609:0.247633:0.000000 1:@0.285317:0.246183:0.293483:0.246183:0.293483:0.231243:0.285317:0.231243:0.000000 4:@0.285317:0.262573:0.293483:0.262573:0.293483:0.247633:0.285317:0.247633:0.000000 a. X = A + B + C.:@0.130229:0.254055:0.314219:0.254055:0.314219:0.237621:0.130229:0.237621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. X = –A + 5B – 2C.:@0.130229:0.303858:0.285500:0.303858:0.285500:0.287425:0.130229:0.287425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.534527:0.152918:0.543547:0.152918:0.543547:0.136249:0.534527:0.136249:0.000000:0.000000 En cada ítem, hallen:@0.564727:0.152918:0.716565:0.152918:0.716565:0.136249:0.564727:0.136249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a, b, c, d.:@0.716403:0.152918:0.776745:0.152918:0.776745:0.136512:0.716403:0.136512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.546301:0.196696:0.561745:0.196696:0.561745:0.180263:0.546301:0.180263:0.000000:0.000000:0.000000 + = .:@0.576503:0.196696:0.850458:0.196696:0.850458:0.180290:0.576503:0.180290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.665336:0.196696:0.674319:0.196696:0.674319:0.180263:0.665336:0.180263:0.000000 3 5:@0.586827:0.184801:0.618321:0.184801:0.618321:0.169861:0.586827:0.169861:0.000000:0.000000:0.000000 a:@0.618254:0.184801:0.626671:0.184801:0.626671:0.169887:0.618254:0.169887:0.000000 2 3:@0.586827:0.206247:0.618321:0.206247:0.618321:0.191307:0.586827:0.191307:0.000000:0.000000:0.000000 c:@0.618254:0.206247:0.625215:0.206247:0.625215:0.191332:0.618254:0.191332:0.000000 b:@0.684793:0.184801:0.693210:0.184801:0.693210:0.169887:0.684793:0.169887:0.000000 2:@0.718935:0.184801:0.727101:0.184801:0.727101:0.169861:0.718935:0.169861:0.000000 2:@0.684798:0.206247:0.692964:0.206247:0.692964:0.191307:0.684798:0.191307:0.000000 d:@0.692897:0.206247:0.701314:0.206247:0.701314:0.191332:0.692897:0.191332:0.000000 9:@0.718951:0.206247:0.727117:0.206247:0.727117:0.191307:0.718951:0.191307:0.000000 0:@0.784588:0.184801:0.792754:0.184801:0.792754:0.169861:0.784588:0.169861:0.000000 0:@0.813325:0.184801:0.821491:0.184801:0.821491:0.169861:0.813325:0.169861:0.000000 0:@0.784593:0.206247:0.792759:0.206247:0.792759:0.191307:0.784593:0.191307:0.000000 0:@0.813325:0.206247:0.821491:0.206247:0.821491:0.191307:0.813325:0.191307:0.000000 b. –3 :@0.545774:0.272399:0.637621:0.272399:0.637621:0.255965:0.545774:0.255965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + + = .:@0.637456:0.272399:0.921535:0.272399:0.921535:0.255993:0.637456:0.255993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.677584:0.272399:0.686566:0.272399:0.686566:0.255965:0.677584:0.255965:0.000000 5:@0.762331:0.272399:0.771313:0.272399:0.771313:0.255965:0.762331:0.255965:0.000000 a:@0.605380:0.258610:0.616743:0.258610:0.616743:0.243696:0.605380:0.243696:0.000000:0.000000 –2:@0.630632:0.258610:0.647098:0.258610:0.647098:0.243670:0.630632:0.243670:0.000000:0.000000 b c:@0.605380:0.280056:0.645173:0.280056:0.645173:0.265141:0.605380:0.265141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.692119:0.258610:0.703481:0.258610:0.703481:0.243696:0.692119:0.243696:0.000000:0.000000 –2:@0.717370:0.258610:0.733836:0.258610:0.733836:0.243670:0.717370:0.243670:0.000000:0.000000 b:@0.692119:0.280056:0.703481:0.280056:0.703481:0.265141:0.692119:0.265141:0.000000:0.000000 4:@0.716115:0.280056:0.724281:0.280056:0.724281:0.265116:0.716115:0.265116:0.000000 c:@0.724214:0.280056:0.731175:0.280056:0.731175:0.265141:0.724214:0.265141:0.000000 1:@0.780094:0.258610:0.791857:0.258610:0.791857:0.243670:0.780094:0.243670:0.000000:0.000000 d:@0.802852:0.258610:0.811269:0.258610:0.811269:0.243696:0.802852:0.243696:0.000000 2:@0.780094:0.280056:0.791857:0.280056:0.791857:0.265116:0.780094:0.265116:0.000000:0.000000 d:@0.802852:0.280056:0.811269:0.280056:0.811269:0.265141:0.802852:0.265141:0.000000 2 –2:@0.861171:0.258610:0.901652:0.258610:0.901652:0.243670:0.861171:0.243670:0.000000:0.000000:0.000000:0.000000:0.000000 3 4:@0.861172:0.280056:0.897502:0.280056:0.897502:0.265116:0.861172:0.265116:0.000000:0.000000:0.000000:0.000000 • :@0.534527:0.338755:0.543547:0.338755:0.543547:0.322085:0.534527:0.322085:0.000000:0.000000 Con los escalares = 4, = –1, = 0, = –2 y :@0.564727:0.338755:0.911831:0.338755:0.911831:0.322085:0.564727:0.322085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.699316:0.338597:0.708435:0.338597:0.708435:0.322937:0.699316:0.322937:0.000000 β:@0.745531:0.338597:0.754580:0.338597:0.754580:0.322937:0.745531:0.322937:0.000000 γ:@0.800879:0.338597:0.808118:0.338597:0.808118:0.322937:0.800879:0.322937:0.000000 λ:@0.845213:0.338597:0.852488:0.338597:0.852488:0.322937:0.845213:0.322937:0.000000 las matrices: :@0.564652:0.355396:0.661168:0.355396:0.661168:0.338727:0.564652:0.338727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.564648:0.393558:0.573634:0.393558:0.573634:0.378643:0.564648:0.378643:0.000000 = , = , = ,:@0.573568:0.393558:0.858746:0.393558:0.858746:0.378618:0.573568:0.378618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.665319:0.393558:0.673352:0.393558:0.673352:0.378643:0.665319:0.378643:0.000000 C:@0.761439:0.393558:0.770441:0.393558:0.770441:0.378643:0.761439:0.378643:0.000000 D:@0.564632:0.438945:0.575107:0.438945:0.575107:0.424030:0.564632:0.424030:0.000000 = , :@0.575040:0.438945:0.682602:0.438945:0.682602:0.424005:0.575040:0.424005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calculen:@0.682405:0.438945:0.739785:0.438945:0.739785:0.423791:0.682405:0.423791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , , , :@0.739685:0.438945:0.801346:0.438945:0.801346:0.424005:0.739685:0.424005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 X X X X:@0.743282:0.438945:0.809495:0.438945:0.809495:0.424030:0.743282:0.424030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.751477:0.441829:0.756238:0.441829:0.756238:0.433119:0.751477:0.433119:0.000000 2:@0.770796:0.441829:0.775557:0.441829:0.775557:0.433119:0.770796:0.433119:0.000000 3:@0.790117:0.441829:0.794878:0.441829:0.794878:0.433119:0.790117:0.433119:0.000000 4:@0.809438:0.441829:0.814199:0.441829:0.814199:0.433119:0.809438:0.433119:0.000000 (que a continuación se definen), mediante :@0.564648:0.478179:0.887788:0.478179:0.887788:0.461510:0.564648:0.461510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la realización de las asociaciones que se :@0.564648:0.494821:0.867867:0.494821:0.867867:0.478151:0.564648:0.478151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 indican::@0.564648:0.511463:0.624490:0.511463:0.624490:0.494793:0.564648:0.494793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 –3:@0.613157:0.385478:0.651845:0.385478:0.651845:0.370538:0.613157:0.370538:0.000000:0.000000:0.000000:0.000000 5:@0.613157:0.406923:0.621323:0.406923:0.621323:0.391983:0.613157:0.391983:0.000000 8:@0.639529:0.406923:0.647695:0.406923:0.647695:0.391983:0.639529:0.391983:0.000000 0 –1:@0.614343:0.431938:0.655399:0.431938:0.655399:0.416998:0.614343:0.416998:0.000000:0.000000:0.000000:0.000000 –1 0:@0.610201:0.453383:0.651249:0.453383:0.651249:0.438443:0.610201:0.438443:0.000000:0.000000:0.000000:0.000000 –3 1:@0.708622:0.387266:0.747300:0.387266:0.747300:0.372326:0.708622:0.372326:0.000000:0.000000:0.000000:0.000000 2:@0.712761:0.408711:0.720928:0.408711:0.720928:0.393771:0.712761:0.393771:0.000000 5:@0.739134:0.408711:0.747300:0.408711:0.747300:0.393771:0.739134:0.393771:0.000000 2 –3:@0.806453:0.382799:0.845138:0.382799:0.845138:0.367859:0.806453:0.367859:0.000000:0.000000:0.000000:0.000000 4 –5:@0.806449:0.404244:0.845138:0.404244:0.845138:0.389304:0.806449:0.389304:0.000000:0.000000:0.000000:0.000000 a. :@0.565934:0.540672:0.581377:0.540672:0.581377:0.524238:0.565934:0.524238:0.000000:0.000000:0.000000 X:@0.596136:0.540672:0.605193:0.540672:0.605193:0.524266:0.596136:0.524266:0.000000 1:@0.605126:0.543844:0.610363:0.543844:0.610363:0.534263:0.605126:0.534263:0.000000 = :@0.610315:0.540672:0.629201:0.540672:0.629201:0.524238:0.610315:0.524238:0.000000:0.000000:0.000000 αA:@0.629109:0.540672:0.648473:0.540672:0.648473:0.524266:0.629109:0.524266:0.000000:0.000000 + [ + ( + :@0.648418:0.540672:0.750008:0.540672:0.750008:0.524238:0.648418:0.524238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 βB:@0.671998:0.540672:0.690239:0.540672:0.690239:0.524266:0.671998:0.524266:0.000000:0.000000 γC:@0.713764:0.540672:0.731177:0.540672:0.731177:0.524266:0.713764:0.524266:0.000000:0.000000 λD:@0.749916:0.540672:0.768986:0.540672:0.768986:0.524266:0.749916:0.524266:0.000000:0.000000 )],:@0.768930:0.540672:0.781742:0.540672:0.781742:0.524238:0.768930:0.524238:0.000000:0.000000:0.000000 b. :@0.565934:0.580480:0.582831:0.580480:0.582831:0.564046:0.565934:0.564046:0.000000:0.000000:0.000000 X:@0.596136:0.580480:0.605193:0.580480:0.605193:0.564074:0.596136:0.564074:0.000000 2:@0.605126:0.583652:0.610363:0.583652:0.610363:0.574071:0.605126:0.574071:0.000000 = [(:@0.610315:0.580480:0.638810:0.580480:0.638810:0.564046:0.610315:0.564046:0.000000:0.000000:0.000000:0.000000:0.000000 αA:@0.638699:0.580480:0.658064:0.580480:0.658064:0.564074:0.638699:0.564074:0.000000:0.000000 + ) + ] + :@0.658008:0.580480:0.759616:0.580480:0.759616:0.564046:0.658008:0.564046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 βB:@0.676802:0.580480:0.695044:0.580480:0.695044:0.564074:0.676802:0.564074:0.000000:0.000000 γC:@0.718568:0.580480:0.735981:0.580480:0.735981:0.564074:0.718568:0.564074:0.000000:0.000000 λD:@0.759506:0.580480:0.778576:0.580480:0.778576:0.564074:0.759506:0.564074:0.000000:0.000000 , :@0.778521:0.580480:0.785755:0.580480:0.785755:0.564046:0.778521:0.564046:0.000000:0.000000 c. :@0.565934:0.620288:0.581009:0.620288:0.581009:0.603854:0.565934:0.603854:0.000000:0.000000:0.000000 X:@0.596136:0.620288:0.605193:0.620288:0.605193:0.603882:0.596136:0.603882:0.000000 3:@0.605126:0.623460:0.610363:0.623460:0.610363:0.613879:0.605126:0.613879:0.000000 = (:@0.610315:0.620288:0.634005:0.620288:0.634005:0.603854:0.610315:0.603854:0.000000:0.000000:0.000000:0.000000 αA:@0.633895:0.620288:0.653259:0.620288:0.653259:0.603882:0.633895:0.603882:0.000000:0.000000 + :@0.653204:0.620288:0.672090:0.620288:0.672090:0.603854:0.653204:0.603854:0.000000:0.000000:0.000000 βD:@0.671998:0.620288:0.692927:0.620288:0.692927:0.603882:0.671998:0.603882:0.000000:0.000000 ) + ( + :@0.692872:0.620288:0.757499:0.620288:0.757499:0.603854:0.692872:0.603854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 γC:@0.721256:0.620288:0.738669:0.620288:0.738669:0.603882:0.721256:0.603882:0.000000:0.000000 λD:@0.757407:0.620288:0.776477:0.620288:0.776477:0.603882:0.757407:0.603882:0.000000:0.000000 ),:@0.776422:0.620288:0.784429:0.620288:0.784429:0.603854:0.776422:0.603854:0.000000:0.000000 d. :@0.565934:0.660095:0.582813:0.660095:0.582813:0.643661:0.565934:0.643661:0.000000:0.000000:0.000000 X:@0.596136:0.660095:0.605193:0.660095:0.605193:0.643688:0.596136:0.643688:0.000000 4:@0.605126:0.663267:0.610363:0.663267:0.610363:0.653686:0.605126:0.653686:0.000000 = (:@0.610315:0.660095:0.634005:0.660095:0.634005:0.643661:0.610315:0.643661:0.000000:0.000000:0.000000:0.000000 αA:@0.633895:0.660095:0.653259:0.660095:0.653259:0.643688:0.633895:0.643688:0.000000:0.000000 + :@0.653204:0.660095:0.672090:0.660095:0.672090:0.643661:0.653204:0.643661:0.000000:0.000000:0.000000 λD:@0.671998:0.660095:0.691068:0.660095:0.691068:0.643688:0.671998:0.643688:0.000000:0.000000 ) + ( + ).:@0.691012:0.660095:0.781742:0.660095:0.781742:0.643661:0.691012:0.643661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 βB:@0.719396:0.660095:0.737638:0.660095:0.737638:0.643688:0.719396:0.643688:0.000000:0.000000 γC:@0.756377:0.660095:0.773790:0.660095:0.773790:0.643688:0.756377:0.643688:0.000000:0.000000 Luego, calculen la matriz X = A + B + C + :@0.564665:0.700895:0.909467:0.700896:0.909467:0.684226:0.564665:0.684225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.790428:0.700738:0.800110:0.700738:0.800110:0.684827:0.790428:0.684827:0.000000 β:@0.831338:0.700738:0.841177:0.700738:0.841177:0.684827:0.831338:0.684827:0.000000 λ:@0.871117:0.700738:0.879411:0.700738:0.879411:0.684827:0.871117:0.684827:0.000000 γ:@0.564648:0.717380:0.572801:0.717380:0.572801:0.701468:0.564648:0.701468:0.000000 D, y comprueben que::@0.572727:0.717538:0.740042:0.717538:0.740042:0.700868:0.572727:0.700868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 X = X = X = X = X = :@0.564647:0.755329:0.713392:0.755334:0.713392:0.738928:0.564647:0.738923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.598647:0.758506:0.603604:0.758506:0.603604:0.748941:0.598647:0.748941:0.000000 2:@0.628689:0.758506:0.633647:0.758506:0.633647:0.748941:0.628689:0.748941:0.000000 3:@0.658730:0.758506:0.663687:0.758506:0.663687:0.748941:0.658730:0.748941:0.000000 4:@0.688772:0.758506:0.693730:0.758506:0.693730:0.748941:0.688772:0.748941:0.000000 11 –11:@0.718635:0.743664:0.772535:0.743664:0.772535:0.728724:0.718635:0.728724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 20:@0.718635:0.765110:0.734900:0.765110:0.734900:0.750170:0.718635:0.750170:0.000000:0.000000 27:@0.752120:0.765110:0.768385:0.765110:0.768385:0.750170:0.752120:0.750170:0.000000:0.000000 :@0.777374:0.755334:0.783651:0.755334:0.783651:0.738928:0.777374:0.738928:0.000000:0.000000 .:@0.783317:0.755019:0.786228:0.755019:0.786228:0.740079:0.783317:0.740079:0.000000 • :@0.537948:0.810674:0.546967:0.810674:0.546967:0.794005:0.537948:0.794005:0.000000:0.000000 Sean :@0.568147:0.810674:0.609247:0.810674:0.609247:0.794005:0.568147:0.794005:0.000000:0.000000:0.000000:0.000000:0.000000 A = :@0.609159:0.810674:0.636420:0.810674:0.636420:0.794268:0.609159:0.794268:0.000000:0.000000:0.000000:0.000000 3 5:@0.643610:0.799005:0.675773:0.799005:0.675773:0.784065:0.643610:0.784065:0.000000:0.000000:0.000000 1 4:@0.643610:0.820450:0.675773:0.820450:0.675773:0.805510:0.643610:0.805510:0.000000:0.000000:0.000000 , B = :@0.682154:0.810674:0.727822:0.810674:0.727822:0.794268:0.682154:0.794268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.737434:0.799897:0.745600:0.799897:0.745600:0.784957:0.737434:0.784957:0.000000 8:@0.766166:0.799897:0.774332:0.799897:0.774332:0.784957:0.766166:0.784957:0.000000 –5 –1:@0.733284:0.821343:0.778482:0.821343:0.778482:0.806403:0.733284:0.806403:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.782835:0.810674:0.786148:0.810674:0.786148:0.794268:0.782835:0.794268:0.000000 . :@0.786081:0.810674:0.797696:0.810674:0.797696:0.794005:0.786081:0.794005:0.000000:0.000000:0.000000 Calculen :@0.568065:0.841614:0.636581:0.841614:0.636581:0.824945:0.568065:0.824945:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y describan cómo obtienen los elemen-:@0.636030:0.841295:0.903203:0.841295:0.903203:0.826141:0.636030:0.826141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tos del producto matricial en forma práctica.:@0.568074:0.856424:0.873043:0.856424:0.873043:0.841270:0.568074:0.841270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. :@0.569491:0.880530:0.584935:0.880530:0.584935:0.864096:0.569491:0.864096:0.000000:0.000000:0.000000 AB. :@0.599694:0.880530:0.653727:0.880530:0.653727:0.864123:0.599694:0.864123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. :@0.653738:0.880530:0.694394:0.880530:0.694394:0.864096:0.653738:0.864096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 BA. AB – BA.:@0.694271:0.880530:0.846101:0.880530:0.846101:0.864123:0.694271:0.864123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c. :@0.771544:0.880530:0.786631:0.880530:0.786631:0.864096:0.771544:0.864096:0.000000:0.000000:0.000000 Trabajo colaborativo:@0.089309:0.677067:0.244769:0.677067:0.244769:0.660397:0.089309:0.660397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Trabajen en equipo, indaguen y resuelvan.:@0.084947:0.706554:0.405337:0.706554:0.405337:0.689885:0.084947:0.689885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.082576:0.733655:0.091595:0.733655:0.091595:0.716986:0.082576:0.716986:0.000000:0.000000 Sean:@0.112775:0.733655:0.150046:0.733655:0.150046:0.716986:0.112775:0.716986:0.000000:0.000000:0.000000:0.000000 A = , B = , C = :@0.112462:0.768243:0.375586:0.768243:0.375586:0.751836:0.112462:0.751836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.343895:0.755325:0.352061:0.755325:0.352061:0.740385:0.343895:0.740385:0.000000 –1:@0.370853:0.755325:0.387320:0.755325:0.387320:0.740385:0.370853:0.740385:0.000000:0.000000 1:@0.343895:0.776770:0.352061:0.776770:0.352061:0.761830:0.343895:0.761830:0.000000 0:@0.375003:0.776770:0.383170:0.776770:0.383170:0.761830:0.375003:0.761830:0.000000 0 1:@0.251728:0.755325:0.283889:0.755325:0.283889:0.740385:0.251728:0.740385:0.000000:0.000000:0.000000 3 1:@0.251727:0.776770:0.283889:0.776770:0.283889:0.761830:0.251727:0.761830:0.000000:0.000000:0.000000 2:@0.156811:0.755325:0.164977:0.755325:0.164977:0.740385:0.156811:0.740385:0.000000 8:@0.185548:0.755325:0.193714:0.755325:0.193714:0.740385:0.185548:0.740385:0.000000 –1 4:@0.152666:0.776770:0.193714:0.776770:0.193714:0.761830:0.152666:0.761830:0.000000:0.000000:0.000000:0.000000 Verifica la igualdad. Para ello, calcula el lado :@0.111037:0.815852:0.479007:0.815852:0.479007:0.799182:0.111037:0.799182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 izquierdo de la igualdad, luego, el lado derecho :@0.111037:0.832494:0.479066:0.832494:0.479066:0.815824:0.111037:0.815824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y, finalmente, compara los resultados.:@0.111037:0.849136:0.394933:0.849136:0.394933:0.832466:0.111037:0.832466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A(B + C) = AB + AC.:@0.108662:0.880187:0.249500:0.880187:0.249500:0.863753:0.108662:0.863753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000