﻿Competencia digital:@0.295776:0.094445:0.678962:0.094445:0.678962:0.027456:0.295776:0.027456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
33:@0.921538:0.966074:0.940353:0.966074:0.940353:0.949450:0.921538:0.949450:0.000000:0.000000
Operaciones con matrices en GeoGebra:@0.368421:0.146762:0.780812:0.146762:0.780812:0.108057:0.368421:0.108057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
GeoGebra permite el ingreso de cualquier matriz. Así, una cuadrada de orden 3 se escribe en la barra de :@0.108033:0.355278:0.814339:0.355278:0.814339:0.339498:0.108033:0.339498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entra-:@0.814339:0.355389:0.854500:0.355389:0.854500:0.339636:0.814339:0.339636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
da:@0.108033:0.371985:0.125374:0.371985:0.125374:0.356232:0.108033:0.356232:0.000000:0.000000
 con la expresión::@0.125374:0.371874:0.242443:0.371874:0.242443:0.356094:0.125374:0.356094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
FórmulaTexto:@0.108033:0.388830:0.201423:0.388830:0.201423:0.372773:0.108033:0.372773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[{{ , , },{ , , },{ , , }}].:@0.201423:0.388471:0.357947:0.388471:0.357947:0.372690:0.201423:0.372690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
102 210 301:@0.218229:0.388678:0.338506:0.388678:0.338506:0.372690:0.218229:0.372690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En :@0.108033:0.421664:0.129059:0.421664:0.129059:0.405883:0.108033:0.405883:0.000000:0.000000:0.000000
Vista Gráfica:@0.129059:0.421774:0.214711:0.421774:0.214711:0.406021:0.129059:0.406021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 se aprecia la nomenclatura de las matrices.:@0.214711:0.421664:0.506142:0.421664:0.506142:0.405883:0.214711:0.405883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para la :@0.108033:0.622286:0.156129:0.622286:0.156129:0.606506:0.108033:0.606506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
suma resta de matrices:@0.156129:0.622493:0.331044:0.622493:0.331044:0.606506:0.156129:0.606506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 o :@0.194201:0.622286:0.211246:0.622286:0.211246:0.606506:0.194201:0.606506:0.000000:0.000000:0.000000
, puedes usar el esquema que sigue::@0.331044:0.622286:0.570582:0.622286:0.570582:0.606506:0.331044:0.606506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.108033:0.638993:0.118813:0.638993:0.118813:0.623240:0.108033:0.623240:0.000000
 = {{ , },{ , }} y   = {{ , },{ ,:@0.118813:0.638882:0.311087:0.638882:0.311087:0.623102:0.118813:0.623102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
21 13:@0.148279:0.639090:0.201517:0.639090:0.201517:0.623102:0.148279:0.623102:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.228126:0.638993:0.236916:0.638993:0.236916:0.623240:0.228126:0.623240:0.000000
60 3–2:@0.266382:0.639090:0.329699:0.639090:0.329699:0.623102:0.266382:0.623102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
}}.:@0.329699:0.638882:0.343538:0.638882:0.343538:0.623102:0.329699:0.623102:0.000000:0.000000:0.000000
Se calcula la matriz   correspondiente a la resta de estas. Así,   = {{ , },{ , }}–{{ , },{ ,:@0.108033:0.672075:0.693218:0.672075:0.693218:0.656295:0.108033:0.656295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.240122:0.672186:0.249723:0.672186:0.249723:0.656433:0.240122:0.656433:0.000000
C:@0.521361:0.672186:0.530962:0.672186:0.530962:0.656433:0.521361:0.656433:0.000000
21 13:@0.560428:0.672283:0.613665:0.672283:0.613665:0.656295:0.560428:0.656295:0.000000:0.000000:0.000000:0.000000:0.000000
60 3–2:@0.648512:0.672283:0.711829:0.672283:0.711829:0.656295:0.648512:0.656295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
}}. Todos los datos :@0.711829:0.672075:0.839715:0.672075:0.839715:0.656295:0.711829:0.656295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son ingresados en la barra de :@0.108033:0.688672:0.308485:0.688672:0.308485:0.672891:0.108033:0.672891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entrada:@0.308485:0.688782:0.361317:0.688782:0.361317:0.673029:0.308485:0.673029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.361321:0.688672:0.363956:0.688672:0.363956:0.672891:0.361321:0.672891:0.000000
Para expresar una matriz real, en la :@0.108033:0.171017:0.344661:0.171017:0.344661:0.155236:0.108033:0.155236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
barra de :@0.108033:0.187613:0.168163:0.187613:0.168163:0.171833:0.108033:0.171833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entrada:@0.168163:0.187724:0.220996:0.187724:0.220996:0.171971:0.168163:0.171971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 escribe la expresión :@0.220995:0.187613:0.361354:0.187613:0.361354:0.171833:0.220995:0.171833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.108033:0.204320:0.118813:0.204320:0.118813:0.188567:0.108033:0.188567:0.000000
 = {{ , },{ , }}, la cual representa a :@0.118813:0.204210:0.352916:0.204210:0.352916:0.188429:0.118813:0.188429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
21 13:@0.148279:0.204417:0.201517:0.204417:0.201517:0.188429:0.148279:0.188429:0.000000:0.000000:0.000000:0.000000:0.000000
la matriz:@0.108033:0.220806:0.165970:0.220806:0.165970:0.205026:0.108033:0.205026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.108033:0.255086:0.119303:0.255086:0.119303:0.238617:0.108033:0.238617:0.000000
 =                    .:@0.119303:0.254970:0.219849:0.254970:0.219849:0.238472:0.119303:0.238472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.153518:0.248131:0.162014:0.248131:0.162014:0.231633:0.153518:0.231633:0.000000
1:@0.191510:0.248131:0.200006:0.248131:0.200006:0.231633:0.191510:0.231633:0.000000
1:@0.153518:0.265944:0.162014:0.265944:0.162014:0.249447:0.153518:0.249447:0.000000
3:@0.191510:0.265944:0.200006:0.265944:0.200006:0.249447:0.191510:0.249447:0.000000
Practica:@0.575978:0.842077:0.633320:0.842077:0.633320:0.826604:0.575978:0.826604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en geogebra operaciones con :@0.633322:0.841654:0.831540:0.841654:0.831540:0.826591:0.633322:0.826591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matrices, para ello puedes emplear las :@0.575978:0.857496:0.824364:0.857496:0.824364:0.842433:0.575978:0.842433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
actividades de la evaluación formativa de :@0.575978:0.873338:0.845966:0.873338:0.845966:0.858275:0.575978:0.858275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las páginas 16 y 17 de este libro.:@0.575978:0.889180:0.779722:0.889180:0.779722:0.874117:0.575978:0.874117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Incluimos en esta sección uno o varios URL de sitios web que, en su momento, estaban en pleno funcionamiento; sin embargo, estos podrían haberse eliminado :@0.108983:0.932250:0.826728:0.932250:0.826728:0.922076:0.108983:0.922076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o cambiado por decisión de los creadores de esos portales. Si tienes algún problema, reporta a: coordinacion@mayaeducacion.com:@0.108983:0.942811:0.696412:0.942811:0.696412:0.932637:0.108983:0.932637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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 :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000