72:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Sistemas de ecuaciones:@0.073089:0.043661:0.282490:0.043661:0.282490:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 6. Determinantes :@0.073089:0.098522:0.422355:0.098522:0.422355:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué tipo de matrices tienen determinantes?:@0.293660:0.172733:0.621245:0.172733:0.621245:0.156300:0.293660:0.156300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6.1 Determinantes de órdenes 2 y 3:@0.293660:0.231243:0.570584:0.231243:0.570584:0.214296:0.293660:0.214296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición de determinante de orden dos:@0.293660:0.258605:0.617400:0.258605:0.617400:0.241658:0.293660:0.241658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   = :@0.293660:0.298005:0.351974:0.298005:0.351974:0.281571:0.293660:0.281571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.323277:0.298005:0.333162:0.298005:0.333162:0.281599:0.323277:0.281599:0.000000
a b:@0.358583:0.288020:0.391844:0.288020:0.391844:0.271614:0.358583:0.271614:0.000000:0.000000:0.000000
c d:@0.359392:0.309460:0.391844:0.309460:0.391844:0.293054:0.359392:0.293054:0.000000:0.000000:0.000000
 una matriz de :@0.398095:0.298011:0.506064:0.298011:0.506064:0.281577:0.398095:0.281577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M:@0.505891:0.298011:0.519770:0.298011:0.519770:0.281605:0.505891:0.281605:0.000000
2×2:@0.519703:0.301183:0.536487:0.301183:0.536487:0.291603:0.519703:0.291603:0.000000:0.000000:0.000000
[ ].:@0.536432:0.298011:0.562441:0.298011:0.562441:0.281577:0.536432:0.281577:0.000000:0.000000:0.000000:0.000000
ℝ:@0.541236:0.298594:0.554526:0.298594:0.554526:0.280939:0.541236:0.280939:0.000000
El determinante de   se nota con det( ) y se define como det( ) =   –  .:@0.293658:0.332515:0.831997:0.332515:0.831997:0.316081:0.293658:0.316081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.436112:0.332515:0.445997:0.332515:0.445997:0.316109:0.436112:0.316109:0.000000
A:@0.567540:0.332515:0.577425:0.332515:0.577425:0.316109:0.567540:0.316109:0.000000
A:@0.743200:0.332515:0.753085:0.332515:0.753085:0.316109:0.743200:0.316109:0.000000
ad bc:@0.776591:0.332515:0.828849:0.332515:0.828849:0.316109:0.776591:0.316109:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios 1:@0.293640:0.367019:0.378074:0.367019:0.378074:0.350350:0.293640:0.350350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.293660:0.402864:0.310668:0.402864:0.310668:0.386194:0.293660:0.386194:0.000000:0.000000:0.000000
Sea A = :@0.323858:0.402864:0.383085:0.402864:0.383085:0.386430:0.323858:0.386430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.392186:0.392878:0.401169:0.392878:0.401169:0.376445:0.392186:0.376445:0.000000
2:@0.420920:0.392878:0.429902:0.392878:0.429902:0.376445:0.420920:0.376445:0.000000
3 –1:@0.392186:0.414319:0.434467:0.414319:0.434467:0.397885:0.392186:0.397885:0.000000:0.000000:0.000000:0.000000
.  Entonces, det( ) = :@0.438651:0.402864:0.586138:0.402864:0.586138:0.386430:0.438651:0.386430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.519633:0.402864:0.523535:0.402864:0.523535:0.386194:0.519633:0.386194:0.000000
A:@0.552637:0.402864:0.562521:0.402864:0.562521:0.386457:0.552637:0.386457:0.000000
1 2:@0.592838:0.392878:0.628180:0.392878:0.628180:0.376445:0.592838:0.376445:0.000000:0.000000:0.000000
3 –1:@0.592838:0.414319:0.632764:0.414319:0.632764:0.397885:0.592838:0.397885:0.000000:0.000000:0.000000:0.000000
 = 1 × (–1) – 3 × 2 = –7.:@0.636808:0.402864:0.804719:0.402864:0.804719:0.386430:0.636808:0.386430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.293660:0.453883:0.310668:0.453883:0.310668:0.437214:0.293660:0.437214:0.000000:0.000000:0.000000
Sea la matriz A = :@0.323858:0.453883:0.448608:0.453883:0.448608:0.437450:0.323858:0.437450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10 5:@0.453187:0.442997:0.495358:0.442997:0.495358:0.426563:0.453187:0.426563:0.000000:0.000000:0.000000:0.000000
1:@0.457642:0.464437:0.466625:0.464437:0.466625:0.448003:0.457642:0.448003:0.000000
2:@0.486376:0.464437:0.495358:0.464437:0.495358:0.448003:0.486376:0.448003:0.000000
.  Se tiene det( ) = :@0.504110:0.453883:0.639842:0.453883:0.639842:0.437450:0.504110:0.437450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.573337:0.453883:0.577239:0.453883:0.577239:0.437214:0.573337:0.437214:0.000000
A:@0.606341:0.453883:0.616225:0.453883:0.616225:0.437477:0.606341:0.437477:0.000000
10 5:@0.645309:0.444786:0.687480:0.444786:0.687480:0.428352:0.645309:0.428352:0.000000:0.000000:0.000000:0.000000
1:@0.649764:0.466226:0.658746:0.466226:0.658746:0.449792:0.649764:0.449792:0.000000
2:@0.678497:0.466226:0.687480:0.466226:0.687480:0.449792:0.678497:0.449792:0.000000
 = 10 × 2 – 1 × 5 = 15.:@0.695730:0.453883:0.853590:0.453883:0.853590:0.437450:0.695730:0.437450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición de determinante de orden tres :@0.293660:0.506264:0.622403:0.506264:0.622403:0.489317:0.293660:0.489317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   = :@0.293660:0.559074:0.351974:0.559074:0.351974:0.542640:0.293660:0.542640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.323277:0.559074:0.333162:0.559074:0.333162:0.542668:0.323277:0.542668:0.000000
a:@0.358159:0.539256:0.367418:0.539256:0.367418:0.522850:0.358159:0.522850:0.000000
11:@0.367359:0.542426:0.377790:0.542426:0.377790:0.532845:0.367359:0.532845:0.000000:0.000000
a:@0.396115:0.539253:0.405374:0.539253:0.405374:0.522847:0.396115:0.522847:0.000000
12:@0.405307:0.542426:0.415738:0.542426:0.415738:0.532845:0.405307:0.532845:0.000000:0.000000
a:@0.434062:0.539253:0.443321:0.539253:0.443321:0.522847:0.434062:0.522847:0.000000
13:@0.443256:0.542426:0.453687:0.542426:0.453687:0.532845:0.443256:0.532845:0.000000:0.000000
a:@0.358168:0.560695:0.367426:0.560695:0.367426:0.544289:0.358168:0.544289:0.000000
21:@0.367359:0.563867:0.377790:0.563867:0.377790:0.554286:0.367359:0.554286:0.000000:0.000000
a:@0.396115:0.560695:0.405374:0.560695:0.405374:0.544289:0.396115:0.544289:0.000000
22:@0.405307:0.563867:0.415738:0.563867:0.415738:0.554286:0.405307:0.554286:0.000000:0.000000
a:@0.434062:0.560695:0.443321:0.560695:0.443321:0.544289:0.434062:0.544289:0.000000
23:@0.443256:0.563867:0.453687:0.563867:0.453687:0.554286:0.443256:0.554286:0.000000:0.000000
a:@0.358168:0.582138:0.367426:0.582138:0.367426:0.565732:0.358168:0.565732:0.000000
31:@0.367359:0.585310:0.377790:0.585310:0.377790:0.575729:0.367359:0.575729:0.000000:0.000000
a:@0.396115:0.582138:0.405374:0.582138:0.405374:0.565732:0.396115:0.565732:0.000000
32:@0.405308:0.585310:0.415739:0.585310:0.415739:0.575729:0.405308:0.575729:0.000000:0.000000
a:@0.434062:0.582138:0.443321:0.582138:0.443321:0.565732:0.434062:0.565732:0.000000
33:@0.443256:0.585310:0.453687:0.585310:0.453687:0.575729:0.443256:0.575729:0.000000:0.000000
  una matriz de :@0.459759:0.559069:0.571686:0.559069:0.571686:0.542635:0.459759:0.542635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M:@0.571506:0.559069:0.585385:0.559069:0.585385:0.542662:0.571506:0.542662:0.000000
3×3:@0.585318:0.562241:0.602102:0.562241:0.602102:0.552660:0.585318:0.552660:0.000000:0.000000:0.000000
[ ].:@0.602047:0.559069:0.628056:0.559069:0.628056:0.542635:0.602047:0.542635:0.000000:0.000000:0.000000:0.000000
ℝ:@0.606851:0.559651:0.620141:0.559651:0.620141:0.541997:0.606851:0.541997:0.000000
El determinante de   se nota con det( ) y se calcula con la siguiente fórmula::@0.293670:0.615027:0.850156:0.615027:0.850156:0.598593:0.293670:0.598593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.436124:0.615027:0.446009:0.615027:0.446009:0.598621:0.436124:0.598621:0.000000
A:@0.567552:0.615027:0.577436:0.615027:0.577436:0.598621:0.567552:0.598621:0.000000
det( ) = :@0.293652:0.650862:0.356328:0.650862:0.356328:0.634428:0.293652:0.634428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.322827:0.650862:0.332712:0.650862:0.332712:0.634456:0.322827:0.634456:0.000000
a:@0.356218:0.650862:0.365477:0.650862:0.365477:0.634456:0.356218:0.634456:0.000000
11:@0.365442:0.654026:0.375873:0.654026:0.375873:0.644445:0.365442:0.644445:0.000000:0.000000
 :@0.375822:0.650853:0.379853:0.650853:0.379853:0.634419:0.375822:0.634419:0.000000
a:@0.384860:0.640868:0.394119:0.640868:0.394119:0.624462:0.384860:0.624462:0.000000
22:@0.394052:0.644037:0.404483:0.644037:0.404483:0.634456:0.394052:0.634456:0.000000:0.000000
a:@0.415970:0.640864:0.425228:0.640864:0.425228:0.624458:0.415970:0.624458:0.000000
23:@0.425162:0.644037:0.435592:0.644037:0.435592:0.634456:0.425162:0.634456:0.000000:0.000000
a:@0.384860:0.662307:0.394119:0.662307:0.394119:0.645901:0.384860:0.645901:0.000000
32:@0.394052:0.665479:0.404483:0.665479:0.404483:0.655899:0.394052:0.655899:0.000000:0.000000
a:@0.415970:0.662307:0.425228:0.662307:0.425228:0.645901:0.415970:0.645901:0.000000
33:@0.425162:0.665479:0.435592:0.665479:0.435592:0.655899:0.425162:0.655899:0.000000:0.000000
  – :@0.440202:0.650853:0.461278:0.650853:0.461278:0.634419:0.440202:0.634419:0.000000:0.000000:0.000000:0.000000
a:@0.461178:0.650853:0.470437:0.650853:0.470437:0.634447:0.461178:0.634447:0.000000
12:@0.470370:0.654026:0.480801:0.654026:0.480801:0.644445:0.470370:0.644445:0.000000:0.000000
  :@0.480750:0.650853:0.488739:0.650853:0.488739:0.634419:0.480750:0.634419:0.000000:0.000000
a:@0.493745:0.641756:0.503004:0.641756:0.503004:0.625350:0.493745:0.625350:0.000000
21:@0.502931:0.644931:0.513361:0.644931:0.513361:0.635350:0.502931:0.635350:0.000000:0.000000
a:@0.524847:0.641758:0.534106:0.641758:0.534106:0.625352:0.524847:0.625352:0.000000
23:@0.534039:0.644931:0.544470:0.644931:0.544470:0.635350:0.534039:0.635350:0.000000:0.000000
a:@0.493737:0.663201:0.502996:0.663201:0.502996:0.646795:0.493737:0.646795:0.000000
31:@0.502931:0.666373:0.513361:0.666373:0.513361:0.656792:0.502931:0.656792:0.000000:0.000000
a:@0.524847:0.663201:0.534106:0.663201:0.534106:0.646795:0.524847:0.646795:0.000000
33:@0.534039:0.666373:0.544470:0.666373:0.544470:0.656792:0.534039:0.656792:0.000000:0.000000
  + :@0.549081:0.650853:0.571924:0.650853:0.571924:0.634419:0.549081:0.634419:0.000000:0.000000:0.000000:0.000000
a:@0.571822:0.650853:0.581081:0.650853:0.581081:0.634447:0.571822:0.634447:0.000000
13 :@0.581014:0.654026:0.593752:0.654026:0.593752:0.644445:0.581014:0.644445:0.000000:0.000000:0.000000
a:@0.598784:0.643545:0.608043:0.643545:0.608043:0.627139:0.598784:0.627139:0.000000
21:@0.607977:0.646717:0.618408:0.646717:0.618408:0.637136:0.607977:0.637136:0.000000:0.000000
a:@0.629894:0.643545:0.639153:0.643545:0.639153:0.627139:0.629894:0.627139:0.000000
22:@0.639086:0.646717:0.649517:0.646717:0.649517:0.637136:0.639086:0.637136:0.000000:0.000000
a:@0.598784:0.664988:0.608043:0.664988:0.608043:0.648581:0.598784:0.648581:0.000000
31:@0.607977:0.668160:0.618408:0.668160:0.618408:0.658579:0.607977:0.658579:0.000000:0.000000
a:@0.629894:0.664988:0.639153:0.664988:0.639153:0.648581:0.629894:0.648581:0.000000
32:@0.639086:0.668160:0.649517:0.668160:0.649517:0.658579:0.639086:0.658579:0.000000:0.000000
Su resultado es:  det( ) = :@0.293660:0.696085:0.476876:0.696085:0.476876:0.679651:0.293660:0.679651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.443375:0.696085:0.453259:0.696085:0.453259:0.679679:0.443375:0.679679:0.000000
a a a:@0.476765:0.696085:0.525183:0.696085:0.525183:0.679679:0.476765:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
11 22 33:@0.485974:0.699257:0.535549:0.699257:0.535549:0.689676:0.485974:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 + :@0.535498:0.696085:0.554384:0.696085:0.554384:0.679651:0.535498:0.679651:0.000000:0.000000:0.000000
a a a:@0.554292:0.696085:0.602691:0.696085:0.602691:0.679679:0.554292:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
12 23 31:@0.563480:0.699257:0.613055:0.699257:0.613055:0.689676:0.563480:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 + :@0.613004:0.696085:0.631890:0.696085:0.631890:0.679651:0.613004:0.679651:0.000000:0.000000:0.000000
a a a:@0.631798:0.696085:0.680199:0.696085:0.680199:0.679679:0.631798:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
21 32 13:@0.640988:0.699257:0.690563:0.699257:0.690563:0.689676:0.640988:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 – :@0.690512:0.696085:0.707631:0.696085:0.707631:0.679651:0.690512:0.679651:0.000000:0.000000:0.000000
a a a:@0.707539:0.696085:0.755938:0.696085:0.755938:0.679679:0.707539:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
13 22 31:@0.716727:0.699257:0.766304:0.699257:0.766304:0.689676:0.716727:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 – :@0.766251:0.696085:0.783370:0.696085:0.783370:0.679651:0.766251:0.679651:0.000000:0.000000:0.000000
a a a:@0.783278:0.696085:0.831679:0.696085:0.831679:0.679679:0.783278:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
12 21 33:@0.792468:0.699257:0.842043:0.699257:0.842043:0.689676:0.792468:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 – :@0.841992:0.696085:0.859111:0.696085:0.859111:0.679651:0.841992:0.679651:0.000000:0.000000:0.000000
a a a:@0.859019:0.696085:0.907418:0.696085:0.907418:0.679679:0.859019:0.679679:0.000000:0.000000:0.000000:0.000000:0.000000
11 23 32:@0.868209:0.699257:0.917784:0.699257:0.917784:0.689676:0.868209:0.689676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.917731:0.696085:0.920934:0.696085:0.920934:0.679651:0.917731:0.679651:0.000000
Ejercicios 2:@0.293652:0.730589:0.378086:0.730589:0.378086:0.713920:0.293652:0.713920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.293660:0.779829:0.310098:0.779829:0.310098:0.763159:0.293660:0.763159:0.000000:0.000000:0.000000
1 4 –3:@0.330448:0.760012:0.395554:0.760012:0.395554:0.743579:0.330448:0.743579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3 –2 1:@0.330466:0.781453:0.390989:0.781453:0.390989:0.765019:0.330466:0.765019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 –1 5:@0.330466:0.802893:0.390989:0.802893:0.390989:0.786459:0.330466:0.786459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.398523:0.779829:0.406254:0.779829:0.406254:0.763159:0.398523:0.763159:0.000000:0.000000
= 1(–2)5 + 3(–1)(–3) + 414 – [4(–2)(–3) + 1(–1)1 + 345]:@0.414144:0.779829:0.781295:0.779829:0.781295:0.763395:0.414144:0.763395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
· ·:@0.569851:0.779829:0.584614:0.779829:0.584614:0.763423:0.569851:0.763423:0.000000:0.000000:0.000000
· ·:@0.753555:0.779829:0.768318:0.779829:0.768318:0.763423:0.753555:0.763423:0.000000:0.000000:0.000000
 :@0.293660:0.821486:0.297691:0.821486:0.297691:0.805053:0.293660:0.805053:0.000000
  = –10 + 9 + 16 – [24 – 1 + 60] = 15 – 83 = –68.:@0.399083:0.820226:0.747809:0.820226:0.747809:0.803792:0.399083:0.803792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b. :@0.293660:0.869826:0.311257:0.869826:0.311257:0.853156:0.293660:0.853156:0.000000:0.000000:0.000000
2 0 –5:@0.331633:0.850903:0.395543:0.850903:0.395543:0.834469:0.331633:0.834469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–7 1 2:@0.327068:0.872344:0.390978:0.872344:0.390978:0.855910:0.327068:0.855910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 4 –3:@0.331633:0.893784:0.395543:0.893784:0.395543:0.877350:0.331633:0.877350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.398523:0.869826:0.402425:0.869826:0.402425:0.853156:0.398523:0.853156:0.000000
= 2 1(–3) + 02 4 + 5(–7)4 – 51 4 – 2 2 4 – 0(–7)(–3):@0.414144:0.869826:0.773177:0.869826:0.773177:0.853392:0.414144:0.853392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
·:@0.437889:0.869826:0.441221:0.869826:0.441221:0.853420:0.437889:0.853420:0.000000
· ·:@0.505002:0.869826:0.520133:0.869826:0.520133:0.853420:0.505002:0.853420:0.000000:0.000000:0.000000
· ·:@0.618741:0.869826:0.633871:0.869826:0.633871:0.853420:0.618741:0.853420:0.000000:0.000000:0.000000
· ·:@0.668256:0.869826:0.683387:0.869826:0.683387:0.853420:0.668256:0.853420:0.000000:0.000000:0.000000
 :@0.293660:0.910223:0.297691:0.910223:0.297691:0.893789:0.293660:0.893789:0.000000
  = –6 + 0 – 140 – 20 – 16 – 0 = –182.:@0.399078:0.910223:0.672076:0.910223:0.672076:0.893789:0.399078:0.893789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.126800:0.143511:0.135055:0.143511:0.135055:0.128882:0.126800:0.128882:0.000000
11:@0.134996:0.146339:0.144297:0.146339:0.144297:0.137797:0.134996:0.137797:0.000000:0.000000
a:@0.162246:0.143511:0.170501:0.143511:0.170501:0.128882:0.162246:0.128882:0.000000
12:@0.170442:0.146339:0.179742:0.146339:0.179742:0.137797:0.170442:0.137797:0.000000:0.000000
a:@0.197693:0.143511:0.205949:0.143511:0.205949:0.128882:0.197693:0.128882:0.000000
13:@0.205889:0.146339:0.215190:0.146339:0.215190:0.137797:0.205889:0.137797:0.000000:0.000000
a:@0.126800:0.163540:0.135055:0.163540:0.135055:0.148912:0.126800:0.148912:0.000000
21:@0.134996:0.166369:0.144297:0.166369:0.144297:0.157826:0.134996:0.157826:0.000000:0.000000
a:@0.162246:0.163540:0.170501:0.163540:0.170501:0.148912:0.162246:0.148912:0.000000
22:@0.170442:0.166369:0.179742:0.166369:0.179742:0.157826:0.170442:0.157826:0.000000:0.000000
a:@0.197693:0.163540:0.205949:0.163540:0.205949:0.148912:0.197693:0.148912:0.000000
23:@0.205889:0.166369:0.215190:0.166369:0.215190:0.157826:0.205889:0.157826:0.000000:0.000000
a:@0.126800:0.183570:0.135055:0.183570:0.135055:0.168941:0.126800:0.168941:0.000000
31:@0.134996:0.186398:0.144297:0.186398:0.144297:0.177855:0.134996:0.177855:0.000000:0.000000
a:@0.162246:0.183570:0.170501:0.183570:0.170501:0.168941:0.162246:0.168941:0.000000
32:@0.170442:0.186398:0.179742:0.186398:0.179742:0.177855:0.170442:0.177855:0.000000:0.000000
a:@0.197693:0.183570:0.205949:0.183570:0.205949:0.168941:0.197693:0.168941:0.000000
33:@0.205889:0.186398:0.215190:0.186398:0.215190:0.177855:0.205889:0.177855:0.000000:0.000000
Competencia :@0.078581:0.232638:0.187141:0.232638:0.187141:0.215691:0.078581:0.215691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.249280:0.176057:0.249280:0.176057:0.232333:0.078581:0.232333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una notación muy :@0.080995:0.272153:0.207355:0.272153:0.207355:0.257213:0.080995:0.257213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
común del determinante :@0.080998:0.287282:0.250642:0.287282:0.250642:0.272342:0.080998:0.272342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la matriz:@0.080998:0.302411:0.157716:0.302411:0.157716:0.287471:0.080998:0.287471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.080998:0.337788:0.089984:0.337788:0.089984:0.322873:0.080998:0.322873:0.000000
 = :@0.089917:0.337788:0.107086:0.337788:0.107086:0.322848:0.089917:0.322848:0.000000:0.000000:0.000000
a b:@0.113923:0.327922:0.146763:0.327922:0.146763:0.312262:0.113923:0.312262:0.000000:0.000000:0.000000
c d:@0.114696:0.349368:0.146763:0.349368:0.146763:0.333707:0.114696:0.333707:0.000000:0.000000:0.000000
 es :@0.153209:0.337789:0.174696:0.337789:0.174696:0.322849:0.153209:0.322849:0.000000:0.000000:0.000000:0.000000
a b:@0.181592:0.328616:0.214431:0.328616:0.214431:0.312955:0.181592:0.312955:0.000000:0.000000:0.000000
c d:@0.182365:0.350061:0.214431:0.350061:0.214431:0.334401:0.182365:0.334401:0.000000:0.000000:0.000000
,  :@0.220548:0.337789:0.230639:0.337789:0.230639:0.322849:0.220548:0.322849:0.000000:0.000000:0.000000
que se lee “determinante :@0.080988:0.371615:0.247992:0.371615:0.247992:0.356675:0.080988:0.356675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la matriz  ”.:@0.080988:0.386744:0.175718:0.386744:0.175718:0.371804:0.080988:0.371804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.161160:0.386744:0.170146:0.386744:0.170146:0.371829:0.161160:0.371829:0.000000
Escribiremos: :@0.080988:0.409021:0.171187:0.409021:0.171187:0.394081:0.080988:0.394081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.080988:0.436556:0.084652:0.436556:0.084652:0.421616:0.080988:0.421616:0.000000
a b:@0.091573:0.427390:0.124413:0.427390:0.124413:0.411730:0.091573:0.411730:0.000000:0.000000:0.000000
c d:@0.092347:0.448835:0.124413:0.448835:0.124413:0.433175:0.092347:0.433175:0.000000:0.000000:0.000000
 =   –  , :@0.130531:0.436563:0.201650:0.436563:0.201650:0.421623:0.130531:0.421623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad bc:@0.147616:0.436563:0.195123:0.436563:0.195123:0.421649:0.147616:0.421649:0.000000:0.000000:0.000000:0.000000:0.000000
o también,   :@0.081015:0.470389:0.162964:0.470389:0.162964:0.455449:0.081015:0.455449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
det( ) =  :@0.081015:0.505072:0.141592:0.505072:0.141592:0.490132:0.081015:0.490132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.107538:0.505072:0.116524:0.505072:0.116524:0.490157:0.107538:0.490157:0.000000
a b:@0.148474:0.495908:0.181313:0.495908:0.181313:0.480247:0.148474:0.480247:0.000000:0.000000:0.000000
c d:@0.149247:0.517353:0.181313:0.517353:0.181313:0.501693:0.149247:0.501693:0.000000:0.000000:0.000000
 =   –  .:@0.187430:0.505081:0.254884:0.505081:0.254884:0.490141:0.187430:0.490141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ad bc:@0.204515:0.505081:0.252023:0.505081:0.252023:0.490166:0.204515:0.490166:0.000000:0.000000:0.000000:0.000000:0.000000
Una estrategia para :@0.081003:0.542487:0.212501:0.542487:0.212501:0.527547:0.081003:0.527547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establecer el determinante :@0.081003:0.557616:0.261893:0.557616:0.261893:0.542676:0.081003:0.542676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de orden tres se :@0.081003:0.572745:0.190347:0.572745:0.190347:0.557805:0.081003:0.557805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representa en esta gráfica::@0.081003:0.587874:0.252875:0.587874:0.252875:0.572934:0.081003:0.572934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Suman::@0.081003:0.613719:0.135087:0.613719:0.135087:0.598313:0.081003:0.598313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.122286:0.635661:0.131124:0.635661:0.131124:0.620001:0.122286:0.620001:0.000000
11:@0.131060:0.638689:0.141017:0.638689:0.141017:0.629543:0.131060:0.629543:0.000000:0.000000
a:@0.160233:0.635661:0.169071:0.635661:0.169071:0.620001:0.160233:0.620001:0.000000
12:@0.169008:0.638689:0.178965:0.638689:0.178965:0.629543:0.169008:0.629543:0.000000:0.000000
a:@0.198182:0.635661:0.207020:0.635661:0.207020:0.620001:0.198182:0.620001:0.000000
13:@0.206955:0.638689:0.216912:0.638689:0.216912:0.629543:0.206955:0.629543:0.000000:0.000000
a:@0.122286:0.657104:0.131124:0.657104:0.131124:0.641444:0.122286:0.641444:0.000000
21:@0.131060:0.660132:0.141017:0.660132:0.141017:0.650986:0.131060:0.650986:0.000000:0.000000
a:@0.160233:0.657104:0.169071:0.657104:0.169071:0.641444:0.160233:0.641444:0.000000
22:@0.169008:0.660132:0.178965:0.660132:0.178965:0.650986:0.169008:0.650986:0.000000:0.000000
a:@0.198182:0.657104:0.207020:0.657104:0.207020:0.641444:0.198182:0.641444:0.000000
23:@0.206955:0.660132:0.216912:0.660132:0.216912:0.650986:0.206955:0.650986:0.000000:0.000000
a:@0.122286:0.678547:0.131124:0.678547:0.131124:0.662886:0.122286:0.662886:0.000000
31:@0.131060:0.681574:0.141017:0.681574:0.141017:0.672429:0.131060:0.672429:0.000000:0.000000
a:@0.160233:0.678547:0.169071:0.678547:0.169071:0.662886:0.160233:0.662886:0.000000
32:@0.169008:0.681574:0.178965:0.681574:0.178965:0.672429:0.169008:0.672429:0.000000:0.000000
a:@0.198182:0.678547:0.207020:0.678547:0.207020:0.662886:0.198182:0.662886:0.000000
33:@0.206955:0.681574:0.216912:0.681574:0.216912:0.672429:0.206955:0.672429:0.000000:0.000000
Restan::@0.080995:0.709996:0.133669:0.709996:0.133669:0.694590:0.080995:0.694590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.122286:0.731934:0.131124:0.731934:0.131124:0.716274:0.122286:0.716274:0.000000
11:@0.131060:0.734963:0.141017:0.734963:0.141017:0.725818:0.131060:0.725818:0.000000:0.000000
a:@0.160233:0.731934:0.169071:0.731934:0.169071:0.716274:0.160233:0.716274:0.000000
12:@0.169008:0.734963:0.178965:0.734963:0.178965:0.725818:0.169008:0.725818:0.000000:0.000000
a:@0.198182:0.731934:0.207020:0.731934:0.207020:0.716274:0.198182:0.716274:0.000000
13:@0.206955:0.734963:0.216912:0.734963:0.216912:0.725818:0.206955:0.725818:0.000000:0.000000
a:@0.122286:0.753377:0.131124:0.753377:0.131124:0.737717:0.122286:0.737717:0.000000
21:@0.131060:0.756406:0.141017:0.756406:0.141017:0.747260:0.131060:0.747260:0.000000:0.000000
a:@0.160233:0.753377:0.169071:0.753377:0.169071:0.737717:0.160233:0.737717:0.000000
22:@0.169008:0.756406:0.178965:0.756406:0.178965:0.747260:0.169008:0.747260:0.000000:0.000000
a:@0.198182:0.753377:0.207020:0.753377:0.207020:0.737717:0.198182:0.737717:0.000000
23:@0.206955:0.756406:0.216912:0.756406:0.216912:0.747260:0.206955:0.747260:0.000000:0.000000
a:@0.122286:0.774820:0.131124:0.774820:0.131124:0.759160:0.122286:0.759160:0.000000
31:@0.131060:0.777847:0.141017:0.777847:0.141017:0.768702:0.131060:0.768702:0.000000:0.000000
a:@0.160233:0.774820:0.169071:0.774820:0.169071:0.759160:0.160233:0.759160:0.000000
32:@0.169008:0.777847:0.178965:0.777847:0.178965:0.768702:0.169008:0.768702:0.000000:0.000000
a:@0.198182:0.774820:0.207020:0.774820:0.207020:0.759160:0.198182:0.759160:0.000000
33:@0.206955:0.777847:0.216912:0.777847:0.216912:0.768702:0.206955:0.768702:0.000000:0.000000
Determinante. :@0.089181:0.851071:0.192284:0.849037:0.191757:0.833888:0.088655:0.835922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matriz :@0.192185:0.849040:0.236702:0.848162:0.236183:0.833227:0.191666:0.834105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrada y, por :@0.089699:0.866196:0.194778:0.864123:0.194259:0.849188:0.089179:0.851262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
extensión, expresión :@0.090224:0.881320:0.229416:0.878574:0.228897:0.863639:0.089705:0.866385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se obtiene a partir :@0.090750:0.896444:0.243388:0.893432:0.242869:0.878498:0.090231:0.881509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de sus elementos :@0.091276:0.911568:0.210591:0.909214:0.210072:0.894279:0.090757:0.896633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicando ciertas reglas.:@0.091801:0.926692:0.248909:0.923592:0.248390:0.908657:0.091282:0.911757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.142235:0.827978:0.201855:0.827978:0.201855:0.812572:0.142235:0.812572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(Ev.) Resuelve determinantes utilizando la definición.:@0.640824:0.971313:0.916213:0.971313:0.916213:0.959362:0.640824:0.959362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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