68:@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
5.6 Matrices especiales:@0.293660:0.136836:0.472941:0.136836:0.472941:0.119889:0.293660:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matriz invertible e inversa:@0.293660:0.167776:0.497042:0.167776:0.497042:0.150829:0.293660:0.150829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.293660:0.198716:0.374781:0.198716:0.374781:0.181769:0.293660:0.181769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.374689:0.198716:0.377892:0.198716:0.377892:0.182282:0.374689:0.182282:0.000000
 :@0.377818:0.198716:0.381628:0.198716:0.381628:0.181769:0.377818:0.181769:0.000000
Sea     :@0.381555:0.198716:0.442004:0.198716:0.442004:0.182282:0.381555:0.182282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.411172:0.198716:0.421057:0.198716:0.421057:0.182310:0.411172:0.182310:0.000000
∈:@0.424941:0.198300:0.438065:0.198300:0.438065:0.181312:0.424941:0.181312:0.000000
M:@0.441931:0.198716:0.455810:0.198716:0.455810:0.182310:0.441931:0.182310:0.000000
2×2 :@0.455726:0.201882:0.474817:0.201882:0.474817:0.192301:0.455726:0.192301:0.000000:0.000000:0.000000:0.000000
[ ].:@0.474759:0.198710:0.500769:0.198710:0.500769:0.182276:0.474759:0.182276:0.000000:0.000000:0.000000:0.000000
ℝ:@0.479563:0.199292:0.492853:0.199292:0.492853:0.181638:0.479563:0.181638:0.000000
i. :@0.293660:0.226073:0.305533:0.226073:0.305533:0.209403:0.293660:0.209403:0.000000:0.000000:0.000000
Se dice que la matriz   es invertible si y solo si existe una matriz     :@0.323858:0.226073:0.816749:0.226073:0.816749:0.209639:0.323858:0.209639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.478350:0.226073:0.488235:0.226073:0.488235:0.209667:0.478350:0.209667:0.000000
B:@0.786837:0.226073:0.795673:0.226073:0.795673:0.209667:0.786837:0.209667:0.000000
∈:@0.799686:0.225657:0.812810:0.225657:0.812810:0.208668:0.799686:0.208668:0.000000
M:@0.816804:0.226073:0.830683:0.226073:0.830683:0.209667:0.816804:0.209667:0.000000
2×2 :@0.830620:0.229245:0.849711:0.229245:0.849711:0.219664:0.830620:0.219664:0.000000:0.000000:0.000000:0.000000
[ ] tal que :@0.849728:0.226073:0.930996:0.226073:0.930996:0.209639:0.849728:0.209639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.854532:0.226655:0.867823:0.226655:0.867823:0.209001:0.854532:0.209001:0.000000
AB:@0.323796:0.242715:0.342443:0.242715:0.342443:0.226309:0.323796:0.226309:0.000000:0.000000
 = :@0.342387:0.242715:0.361273:0.242715:0.361273:0.226281:0.342387:0.226281:0.000000:0.000000:0.000000
BA:@0.361181:0.242715:0.380049:0.242715:0.380049:0.226309:0.361181:0.226309:0.000000:0.000000
 =  .:@0.379993:0.242715:0.406543:0.242715:0.406543:0.226281:0.379993:0.226281:0.000000:0.000000:0.000000:0.000000:0.000000
ii. :@0.293660:0.267577:0.309766:0.267577:0.309766:0.250907:0.293660:0.250907:0.000000:0.000000:0.000000:0.000000
Se dice que   es singular si y solo si   no es invertible, y que   es no singular si y solo :@0.323858:0.267577:0.931095:0.267577:0.931095:0.251143:0.323858:0.251143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.411403:0.267577:0.421288:0.267577:0.421288:0.251171:0.411403:0.251171:0.000000
A:@0.579148:0.267577:0.589033:0.267577:0.589033:0.251171:0.579148:0.251171:0.000000
A:@0.753815:0.267577:0.763699:0.267577:0.763699:0.251171:0.753815:0.251171:0.000000
si   es invertible.:@0.323766:0.284219:0.442982:0.284219:0.442982:0.267785:0.323766:0.267785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.338271:0.284219:0.348156:0.284219:0.348156:0.267812:0.338271:0.267812:0.000000
Si   es invertible su inversa se nota :@0.323766:0.309084:0.577827:0.309084:0.577827:0.292650:0.323766:0.292650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.339946:0.309084:0.349831:0.309084:0.349831:0.292678:0.339946:0.292678:0.000000
A:@0.577547:0.309084:0.587432:0.309084:0.587432:0.292678:0.577547:0.292678:0.000000
–1:@0.587386:0.303017:0.597946:0.303017:0.597946:0.293436:0.587386:0.293436:0.000000:0.000000
, es decir que,   = :@0.597895:0.309080:0.727501:0.309080:0.727501:0.292647:0.597895:0.292647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.699853:0.309080:0.708688:0.309080:0.708688:0.292674:0.699853:0.292674:0.000000
A:@0.727409:0.309080:0.737293:0.309080:0.737293:0.292674:0.727409:0.292674:0.000000
–1:@0.737230:0.303017:0.747789:0.303017:0.747789:0.293436:0.737230:0.293436:0.000000:0.000000
. Luego, :@0.747739:0.309080:0.807715:0.309080:0.807715:0.292647:0.747739:0.292647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AA:@0.807599:0.309080:0.827184:0.309080:0.827184:0.292674:0.807599:0.292674:0.000000:0.000000
–1:@0.827117:0.303017:0.837677:0.303017:0.837677:0.293436:0.827117:0.293436:0.000000:0.000000
 = :@0.837626:0.309080:0.856512:0.309080:0.856512:0.292647:0.837626:0.292647:0.000000:0.000000:0.000000
A A:@0.856420:0.309080:0.886630:0.309080:0.886630:0.292674:0.856420:0.292674:0.000000:0.000000:0.000000
–1:@0.866236:0.303017:0.876796:0.303017:0.876796:0.293436:0.866236:0.293436:0.000000:0.000000
 =  .:@0.886556:0.309080:0.913138:0.309080:0.913138:0.292647:0.886556:0.292647:0.000000:0.000000:0.000000:0.000000:0.000000
A la matriz :@0.323781:0.336444:0.404029:0.336444:0.404029:0.320010:0.323781:0.320010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.403871:0.336444:0.413756:0.336444:0.413756:0.320038:0.403871:0.320038:0.000000
–1:@0.413695:0.330378:0.424255:0.330378:0.424255:0.320798:0.413695:0.320798:0.000000:0.000000
 se le llama matriz inversa de  .:@0.424204:0.336444:0.647337:0.336444:0.647337:0.320010:0.424204:0.320010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.634323:0.336444:0.644208:0.336444:0.644208:0.320038:0.634323:0.320038:0.000000
Ejercicio 7:@0.293660:0.370948:0.370805:0.370948:0.370805:0.354278:0.293660:0.354278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean   = :@0.293660:0.398740:0.361767:0.398740:0.361767:0.382306:0.293660:0.382306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.333070:0.398740:0.342955:0.398740:0.342955:0.382334:0.333070:0.382334:0.000000
1:@0.371310:0.388862:0.379476:0.388862:0.379476:0.373922:0.371310:0.373922:0.000000
3:@0.400042:0.388862:0.408208:0.388862:0.408208:0.373922:0.400042:0.373922:0.000000
0:@0.371310:0.410307:0.379476:0.410307:0.379476:0.395367:0.371310:0.395367:0.000000
1:@0.400042:0.410307:0.408208:0.410307:0.408208:0.395367:0.400042:0.395367:0.000000
,    = :@0.417369:0.398743:0.456039:0.398743:0.456039:0.382310:0.417369:0.382310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.428391:0.398743:0.437227:0.398743:0.437227:0.382337:0.428391:0.382337:0.000000
1 –3:@0.465581:0.388862:0.506645:0.388862:0.506645:0.373922:0.465581:0.373922:0.000000:0.000000:0.000000:0.000000
0:@0.465581:0.410307:0.473747:0.410307:0.473747:0.395367:0.465581:0.395367:0.000000
1:@0.494313:0.410307:0.502479:0.410307:0.502479:0.395367:0.494313:0.395367:0.000000
  Si: :@0.511639:0.398743:0.538955:0.398743:0.538955:0.382310:0.511639:0.382310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.538840:0.398743:0.557486:0.398743:0.557486:0.382337:0.538840:0.382337:0.000000:0.000000
 = :@0.557431:0.398743:0.576317:0.398743:0.576317:0.382310:0.557431:0.382310:0.000000:0.000000:0.000000
BA =     B = A:@0.576225:0.398743:0.677972:0.398743:0.677972:0.382337:0.576225:0.382337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.620633:0.398327:0.638801:0.398327:0.638801:0.381339:0.620633:0.381339:0.000000
–1:@0.677938:0.392679:0.688498:0.392679:0.688498:0.383099:0.677938:0.383099:0.000000:0.000000
.:@0.688447:0.398743:0.691650:0.398743:0.691650:0.382310:0.688447:0.382310:0.000000
AB:@0.293667:0.452441:0.312313:0.452441:0.312313:0.436035:0.293667:0.436035:0.000000:0.000000
 = :@0.312258:0.452441:0.331144:0.452441:0.331144:0.436007:0.312258:0.436007:0.000000:0.000000:0.000000
1 + 0:@0.339938:0.442561:0.373305:0.442561:0.373305:0.427621:0.339938:0.427621:0.000000:0.000000:0.000000:0.000000:0.000000
–3 + 3:@0.392984:0.442561:0.434651:0.442561:0.434651:0.427621:0.392984:0.427621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 + 0:@0.339938:0.464006:0.373305:0.464006:0.373305:0.449066:0.339938:0.449066:0.000000:0.000000:0.000000:0.000000:0.000000
0 + 1:@0.397134:0.464006:0.430501:0.464006:0.430501:0.449066:0.397134:0.449066:0.000000:0.000000:0.000000:0.000000:0.000000
 , :@0.443646:0.452444:0.454764:0.452444:0.454764:0.436010:0.443646:0.436010:0.000000:0.000000:0.000000
AB:@0.454670:0.452444:0.473317:0.452444:0.473317:0.436037:0.454670:0.436037:0.000000:0.000000
 = :@0.473261:0.452444:0.492147:0.452444:0.492147:0.436010:0.473261:0.436010:0.000000:0.000000:0.000000
1 0:@0.499304:0.442561:0.531467:0.442561:0.531467:0.427621:0.499304:0.427621:0.000000:0.000000:0.000000
0 1:@0.499304:0.464006:0.531467:0.464006:0.531467:0.449066:0.499304:0.449066:0.000000:0.000000:0.000000
. Por lo tanto,   = :@0.538247:0.452444:0.663765:0.452444:0.663765:0.436010:0.538247:0.436010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.636117:0.452444:0.644953:0.452444:0.644953:0.436037:0.636117:0.436037:0.000000
A:@0.663673:0.452444:0.673557:0.452444:0.673557:0.436037:0.663673:0.436037:0.000000
–1:@0.673495:0.446380:0.684055:0.446380:0.684055:0.436799:0.673495:0.436799:0.000000:0.000000
 = :@0.684003:0.452444:0.702889:0.452444:0.702889:0.436010:0.684003:0.436010:0.000000:0.000000:0.000000
1 –3:@0.710051:0.441668:0.748739:0.441668:0.748739:0.426728:0.710051:0.426728:0.000000:0.000000:0.000000:0.000000
0:@0.710051:0.463113:0.718217:0.463113:0.718217:0.448173:0.710051:0.448173:0.000000
1:@0.736423:0.463113:0.744589:0.463113:0.744589:0.448173:0.736423:0.448173:0.000000
.:@0.753738:0.452444:0.756941:0.452444:0.756941:0.436010:0.753738:0.436010:0.000000
5.7 Potencia de matrices:@0.293660:0.504822:0.484424:0.504822:0.484424:0.487876:0.293660:0.487876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición.:@0.293660:0.532184:0.379051:0.532184:0.379051:0.515237:0.293660:0.515237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sea     :@0.378941:0.532184:0.443348:0.532184:0.443348:0.515751:0.378941:0.515751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.412516:0.532184:0.422400:0.532184:0.422400:0.515778:0.412516:0.515778:0.000000
∈:@0.426284:0.531768:0.439409:0.531768:0.439409:0.514780:0.426284:0.514780:0.000000
M:@0.443274:0.532184:0.457153:0.532184:0.457153:0.515778:0.443274:0.515778:0.000000
2×2:@0.457088:0.535358:0.473872:0.535358:0.473872:0.525777:0.457088:0.525777:0.000000:0.000000:0.000000
[ ] con   ≠ 0.:@0.473817:0.532186:0.572885:0.532186:0.572885:0.515752:0.473817:0.515752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.478621:0.532768:0.491911:0.532768:0.491911:0.515114:0.478621:0.515114:0.000000
A:@0.532150:0.532186:0.542034:0.532186:0.542034:0.515780:0.532150:0.515780:0.000000
i. :@0.293660:0.559549:0.305533:0.559549:0.305533:0.542879:0.293660:0.542879:0.000000:0.000000:0.000000
Se define :@0.323860:0.559549:0.395217:0.559549:0.395217:0.543115:0.323860:0.543115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.395077:0.559549:0.404962:0.559549:0.404962:0.543143:0.395077:0.543143:0.000000
m:@0.404899:0.553485:0.413687:0.553485:0.413687:0.543904:0.404899:0.543904:0.000000
 recursivamente como sigue:   =  ,  :@0.413640:0.559549:0.676221:0.559549:0.676221:0.543115:0.413640:0.543115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.626336:0.559549:0.636221:0.559549:0.636221:0.543143:0.626336:0.543143:0.000000
0:@0.636162:0.553485:0.641399:0.553485:0.641399:0.543904:0.636162:0.543904:0.000000
A:@0.676126:0.559549:0.686011:0.559549:0.686011:0.543143:0.676126:0.543143:0.000000
m+1:@0.685944:0.553485:0.706280:0.553485:0.706280:0.543904:0.685944:0.543904:0.000000:0.000000:0.000000
 = :@0.706225:0.559549:0.725111:0.559549:0.725111:0.543115:0.706225:0.543115:0.000000:0.000000:0.000000
A A:@0.725019:0.559549:0.753462:0.559549:0.753462:0.543143:0.725019:0.543143:0.000000:0.000000:0.000000
m:@0.734835:0.553485:0.743624:0.553485:0.743624:0.543904:0.734835:0.543904:0.000000
, :@0.753388:0.559549:0.760622:0.559549:0.760622:0.543115:0.753388:0.543115:0.000000:0.000000
m:@0.323781:0.579769:0.338396:0.579769:0.338396:0.563363:0.323781:0.563363:0.000000
 = 0, 1, … .:@0.338323:0.579769:0.414621:0.579769:0.414621:0.563335:0.338323:0.563335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii. :@0.293660:0.607128:0.309766:0.607128:0.309766:0.590459:0.293660:0.590459:0.000000:0.000000:0.000000:0.000000
Si   es invertible, se define A  = (A ) , m = 0, 1, … .:@0.323860:0.607128:0.699356:0.607128:0.699356:0.590694:0.323860:0.590694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.340040:0.607128:0.349924:0.607128:0.349924:0.590722:0.340040:0.590722:0.000000
–m:@0.528696:0.601064:0.542807:0.601064:0.542807:0.591483:0.528696:0.591483:0.000000:0.000000
–1 m:@0.576921:0.601064:0.601016:0.601064:0.601016:0.591483:0.576921:0.591483:0.000000:0.000000:0.000000:0.000000
De la definición: :@0.323774:0.631994:0.444132:0.631994:0.444132:0.615560:0.323774:0.615560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.323774:0.659356:0.333659:0.659356:0.333659:0.642950:0.323774:0.642950:0.000000
1:@0.333599:0.653289:0.338836:0.653289:0.338836:0.643708:0.333599:0.643708:0.000000
 = :@0.338790:0.659353:0.357676:0.659353:0.357676:0.642919:0.338790:0.642919:0.000000:0.000000:0.000000
A:@0.357583:0.659353:0.367468:0.659353:0.367468:0.642947:0.357583:0.642947:0.000000
0+1:@0.367398:0.653289:0.384182:0.653289:0.384182:0.643708:0.367398:0.643708:0.000000:0.000000:0.000000
 = :@0.384127:0.659353:0.403013:0.659353:0.403013:0.642919:0.384127:0.642919:0.000000:0.000000:0.000000
A A =  A = A, :@0.402921:0.659353:0.493672:0.659353:0.493672:0.642947:0.402921:0.642947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.412735:0.653289:0.417972:0.653289:0.417972:0.643708:0.412735:0.643708:0.000000
A:@0.534628:0.659353:0.544513:0.659353:0.544513:0.642947:0.534628:0.642947:0.000000
2:@0.544446:0.653289:0.549682:0.653289:0.549682:0.643708:0.544446:0.643708:0.000000
 = :@0.549636:0.659353:0.568522:0.659353:0.568522:0.642919:0.549636:0.642919:0.000000:0.000000:0.000000
A:@0.568430:0.659353:0.578315:0.659353:0.578315:0.642947:0.568430:0.642947:0.000000
1+1:@0.578245:0.653289:0.595029:0.653289:0.595029:0.643708:0.578245:0.643708:0.000000:0.000000:0.000000
 = :@0.594973:0.659353:0.613859:0.659353:0.613859:0.642919:0.594973:0.642919:0.000000:0.000000:0.000000
A A = AA,:@0.613767:0.659353:0.678809:0.659353:0.678809:0.642947:0.613767:0.642947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.623582:0.653289:0.628819:0.653289:0.628819:0.643708:0.623582:0.643708:0.000000
A:@0.323783:0.679573:0.333667:0.679573:0.333667:0.663167:0.323783:0.663167:0.000000
3:@0.333599:0.673504:0.338836:0.673504:0.338836:0.663923:0.333599:0.663923:0.000000
 = :@0.338790:0.679568:0.357676:0.679568:0.357676:0.663134:0.338790:0.663134:0.000000:0.000000:0.000000
A:@0.357583:0.679568:0.367468:0.679568:0.367468:0.663162:0.357583:0.663162:0.000000
2+1:@0.367398:0.673504:0.384182:0.673504:0.384182:0.663923:0.367398:0.663923:0.000000:0.000000:0.000000
 = :@0.384127:0.679568:0.403013:0.679568:0.403013:0.663134:0.384127:0.663134:0.000000:0.000000:0.000000
A A = AAA, :@0.402921:0.679568:0.480910:0.679568:0.480910:0.663162:0.402921:0.663162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.412735:0.673504:0.417972:0.673504:0.417972:0.663923:0.412735:0.663923:0.000000
A:@0.534628:0.679568:0.544513:0.679568:0.544513:0.663162:0.534628:0.663162:0.000000
4:@0.544446:0.673504:0.549682:0.673504:0.549682:0.663923:0.544446:0.663923:0.000000
 = :@0.549635:0.679568:0.568521:0.679568:0.568521:0.663134:0.549635:0.663134:0.000000:0.000000:0.000000
A:@0.568429:0.679568:0.578313:0.679568:0.578313:0.663162:0.568429:0.663162:0.000000
3+1:@0.578245:0.673504:0.595029:0.673504:0.595029:0.663923:0.578245:0.663923:0.000000:0.000000:0.000000
 = :@0.594973:0.679568:0.613859:0.679568:0.613859:0.663134:0.594973:0.663134:0.000000:0.000000:0.000000
A A = AAAA, :@0.613767:0.679568:0.701465:0.679568:0.701465:0.663162:0.613767:0.663162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.623582:0.673504:0.628819:0.673504:0.628819:0.663923:0.623582:0.663923:0.000000
y así sucesivamente.:@0.701444:0.679568:0.847823:0.679568:0.847823:0.663134:0.701444:0.663134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es invertible, :@0.323783:0.706930:0.448628:0.706930:0.448628:0.690496:0.323783:0.690496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.339963:0.706930:0.349847:0.706930:0.349847:0.690524:0.339963:0.690524:0.000000
A:@0.448473:0.706930:0.458358:0.706930:0.458358:0.690524:0.448473:0.690524:0.000000
–1:@0.458290:0.700867:0.468849:0.700867:0.468849:0.691286:0.458290:0.691286:0.000000:0.000000
 = (:@0.468798:0.706931:0.492489:0.706931:0.492489:0.690497:0.468798:0.690497:0.000000:0.000000:0.000000:0.000000
A:@0.492378:0.706931:0.502263:0.706931:0.502263:0.690525:0.492378:0.690525:0.000000
–1 1:@0.502206:0.700867:0.522748:0.700867:0.522748:0.691286:0.502206:0.691286:0.000000:0.000000:0.000000:0.000000
):@0.512713:0.706931:0.517591:0.706931:0.517591:0.690497:0.512713:0.690497:0.000000
,  A:@0.522702:0.706931:0.544514:0.706931:0.544514:0.690525:0.522702:0.690525:0.000000:0.000000:0.000000:0.000000
–2:@0.544446:0.700867:0.555005:0.700867:0.555005:0.691286:0.544446:0.691286:0.000000:0.000000
 = (:@0.554954:0.706931:0.578645:0.706931:0.578645:0.690497:0.554954:0.690497:0.000000:0.000000:0.000000:0.000000
A:@0.578534:0.706931:0.588419:0.706931:0.588419:0.690525:0.578534:0.690525:0.000000
–1 2:@0.588360:0.700867:0.608904:0.700867:0.608904:0.691286:0.588360:0.691286:0.000000:0.000000:0.000000:0.000000
)  = :@0.598869:0.706931:0.627742:0.706931:0.627742:0.690497:0.598869:0.690497:0.000000:0.000000:0.000000:0.000000:0.000000
A A ,:@0.627650:0.706931:0.671633:0.706931:0.671633:0.690525:0.627650:0.690525:0.000000:0.000000:0.000000:0.000000:0.000000
–1 –1:@0.637466:0.700867:0.668352:0.700867:0.668352:0.691286:0.637466:0.691286:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.323773:0.727151:0.333657:0.727151:0.333657:0.710745:0.323773:0.710745:0.000000
–3:@0.333599:0.721083:0.344159:0.721083:0.344159:0.711502:0.333599:0.711502:0.000000:0.000000
 = (:@0.344108:0.727147:0.367798:0.727147:0.367798:0.710713:0.344108:0.710713:0.000000:0.000000:0.000000:0.000000
A:@0.367687:0.727147:0.377572:0.727147:0.377572:0.710741:0.367687:0.710741:0.000000
–1 3:@0.377514:0.721083:0.398057:0.721083:0.398057:0.711502:0.377514:0.711502:0.000000:0.000000:0.000000:0.000000
)  = :@0.388022:0.727147:0.416895:0.727147:0.416895:0.710713:0.388022:0.710713:0.000000:0.000000:0.000000:0.000000:0.000000
A A A , :@0.416803:0.727147:0.484353:0.727147:0.484353:0.710741:0.416803:0.710741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–1 –1 –1:@0.426619:0.721083:0.477832:0.721083:0.477832:0.711502:0.426619:0.711502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.484292:0.727147:0.488324:0.727147:0.488324:0.710713:0.484292:0.710713:0.000000
A:@0.534628:0.727147:0.544513:0.727147:0.544513:0.710741:0.534628:0.710741:0.000000
–4:@0.544446:0.721083:0.555005:0.721083:0.555005:0.711502:0.544446:0.711502:0.000000:0.000000
 = (:@0.554954:0.727147:0.578645:0.727147:0.578645:0.710713:0.554954:0.710713:0.000000:0.000000:0.000000:0.000000
A:@0.578534:0.727147:0.588419:0.727147:0.588419:0.710741:0.578534:0.710741:0.000000
–1 4:@0.588360:0.721083:0.608904:0.721083:0.608904:0.711502:0.588360:0.711502:0.000000:0.000000:0.000000:0.000000
)  = :@0.598869:0.727147:0.627742:0.727147:0.627742:0.710713:0.598869:0.710713:0.000000:0.000000:0.000000:0.000000:0.000000
A A A A , :@0.627650:0.727147:0.715526:0.727147:0.715526:0.710741:0.627650:0.710741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–1 –1 –1 –1:@0.637466:0.721083:0.709005:0.721083:0.709005:0.711502:0.637466:0.711502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y así, sucesivamente.:@0.715471:0.727147:0.864978:0.727147:0.864978:0.710713:0.715471:0.710713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio 8:@0.293668:0.761651:0.370813:0.761651:0.370813:0.744982:0.293668:0.744982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la matriz   = :@0.293668:0.807305:0.417457:0.807305:0.417457:0.790872:0.293668:0.790872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.388760:0.807305:0.398645:0.807305:0.398645:0.790899:0.388760:0.790899:0.000000
–:@0.464548:0.792073:0.472915:0.792073:0.472915:0.777133:0.464548:0.777133:0.000000
1:@0.433177:0.783811:0.441343:0.783811:0.441343:0.768872:0.433177:0.768872:0.000000
2:@0.433177:0.800201:0.441343:0.800201:0.441343:0.785261:0.433177:0.785261:0.000000
1:@0.476123:0.815909:0.484289:0.815909:0.484289:0.800969:0.476123:0.800969:0.000000
2:@0.476123:0.832298:0.484289:0.832298:0.484289:0.817359:0.476123:0.817359:0.000000
 3:@0.480045:0.783811:0.491809:0.783811:0.491809:0.768872:0.480045:0.768872:0.000000:0.000000
2:@0.481836:0.800201:0.490002:0.800201:0.490002:0.785261:0.481836:0.785261:0.000000
 3:@0.431382:0.815909:0.443145:0.815909:0.443145:0.800969:0.431382:0.800969:0.000000:0.000000
2:@0.433172:0.832298:0.441338:0.832298:0.441338:0.817359:0.433172:0.817359:0.000000
, calcula  .:@0.501503:0.807317:0.580885:0.807317:0.580885:0.790883:0.501503:0.790883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.562674:0.807317:0.572558:0.807317:0.572558:0.790911:0.562674:0.790911:0.000000
2:@0.572492:0.801253:0.577728:0.801253:0.577728:0.791672:0.572492:0.791672:0.000000
A:@0.293658:0.883911:0.303543:0.883911:0.303543:0.867505:0.293658:0.867505:0.000000
2:@0.303478:0.877848:0.308715:0.877848:0.308715:0.868267:0.303478:0.868267:0.000000
 = :@0.308667:0.883912:0.327553:0.883912:0.327553:0.867478:0.308667:0.867478:0.000000:0.000000:0.000000
AA:@0.327461:0.883912:0.347046:0.883912:0.347046:0.867506:0.327461:0.867506:0.000000:0.000000
 = :@0.346991:0.883912:0.365877:0.883912:0.365877:0.867478:0.346991:0.867478:0.000000:0.000000:0.000000
–:@0.412968:0.868668:0.421335:0.868668:0.421335:0.853729:0.412968:0.853729:0.000000
–:@0.503330:0.868668:0.511697:0.868668:0.511697:0.853729:0.503330:0.853729:0.000000
1:@0.381598:0.860408:0.389764:0.860408:0.389764:0.845468:0.381598:0.845468:0.000000
2:@0.381598:0.876798:0.389764:0.876798:0.389764:0.861858:0.381598:0.861858:0.000000
1:@0.471961:0.860408:0.480127:0.860408:0.480127:0.845468:0.471961:0.845468:0.000000
2:@0.471961:0.876798:0.480127:0.876798:0.480127:0.861858:0.471961:0.861858:0.000000
1:@0.424544:0.892504:0.432710:0.892504:0.432710:0.877564:0.424544:0.877564:0.000000
2:@0.424544:0.908894:0.432710:0.908894:0.432710:0.893954:0.424544:0.893954:0.000000
1:@0.514907:0.892504:0.523073:0.892504:0.523073:0.877564:0.514907:0.877564:0.000000
2:@0.514907:0.908894:0.523073:0.908894:0.523073:0.893954:0.514907:0.893954:0.000000
 3:@0.428466:0.860408:0.440230:0.860408:0.440230:0.845468:0.428466:0.845468:0.000000:0.000000
2:@0.430257:0.876798:0.438423:0.876798:0.438423:0.861858:0.430257:0.861858:0.000000
 3:@0.518829:0.860408:0.530593:0.860408:0.530593:0.845468:0.518829:0.845468:0.000000:0.000000
2:@0.520620:0.876798:0.528786:0.876798:0.528786:0.861858:0.520620:0.861858:0.000000
 3:@0.379803:0.892504:0.391567:0.892504:0.391567:0.877564:0.379803:0.877564:0.000000:0.000000
2:@0.381593:0.908894:0.389759:0.908894:0.389759:0.893954:0.381593:0.893954:0.000000
 3:@0.470166:0.892504:0.481930:0.892504:0.481930:0.877564:0.470166:0.877564:0.000000:0.000000
2:@0.471956:0.908894:0.480122:0.908894:0.480122:0.893954:0.471956:0.893954:0.000000
 = :@0.540286:0.883912:0.559171:0.883912:0.559171:0.867478:0.540286:0.867478:0.000000:0.000000:0.000000
–:@0.563301:0.869562:0.571668:0.869562:0.571668:0.854622:0.563301:0.854622:0.000000
–:@0.611013:0.869562:0.619380:0.869562:0.619380:0.854622:0.611013:0.854622:0.000000
–:@0.611013:0.901724:0.619380:0.901724:0.619380:0.886784:0.611013:0.886784:0.000000
1:@0.579920:0.861301:0.588086:0.861301:0.588086:0.846361:0.579920:0.846361:0.000000
2:@0.579920:0.877690:0.588086:0.877690:0.588086:0.862751:0.579920:0.862751:0.000000
1:@0.626212:0.893398:0.634378:0.893398:0.634378:0.878458:0.626212:0.878458:0.000000
2:@0.626212:0.909788:0.634378:0.909788:0.634378:0.894848:0.626212:0.894848:0.000000
 3:@0.626788:0.861301:0.638552:0.861301:0.638552:0.846361:0.626788:0.846361:0.000000:0.000000
2:@0.628578:0.877690:0.636745:0.877690:0.636745:0.862751:0.628578:0.862751:0.000000
 3:@0.576451:0.893398:0.588215:0.893398:0.588215:0.878458:0.576451:0.878458:0.000000:0.000000
2:@0.578241:0.909788:0.586407:0.909788:0.586407:0.894848:0.578241:0.894848:0.000000
.:@0.652712:0.883912:0.655915:0.883912:0.655915:0.867478:0.652712:0.867478:0.000000
Competencia :@0.078581:0.146688:0.187141:0.146688:0.187141:0.129741:0.078581:0.129741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.163330:0.176057:0.163330:0.176057:0.146383:0.078581:0.146383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea     :@0.080995:0.189116:0.135956:0.189116:0.135956:0.174176:0.080995:0.174176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.107927:0.189116:0.116913:0.189116:0.116913:0.174201:0.107927:0.174201:0.000000
∈:@0.120444:0.188737:0.132375:0.188737:0.132375:0.173293:0.120444:0.173293:0.000000
M:@0.135889:0.189116:0.148506:0.189116:0.148506:0.174201:0.135889:0.174201:0.000000
2×2:@0.148439:0.191999:0.163697:0.191999:0.163697:0.183290:0.148439:0.183290:0.000000:0.000000:0.000000
 [ ]. Si   es :@0.163646:0.189116:0.239568:0.189116:0.239568:0.174176:0.163646:0.174176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.171595:0.189645:0.183677:0.189645:0.183677:0.173596:0.171595:0.173596:0.000000
A:@0.209096:0.189116:0.218082:0.189116:0.218082:0.174201:0.209096:0.174201:0.000000
invertible, :@0.080998:0.204244:0.149448:0.204244:0.149448:0.189305:0.080998:0.189305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.149322:0.204244:0.158308:0.204244:0.158308:0.189330:0.149322:0.189330:0.000000
–1:@0.158251:0.198732:0.167851:0.198732:0.167851:0.190022:0.158251:0.190022:0.000000:0.000000
 es única. :@0.167805:0.204244:0.231879:0.204244:0.231879:0.189305:0.167805:0.189305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se dice que   es singular si :@0.080989:0.219373:0.260828:0.219373:0.260828:0.204434:0.080989:0.204434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.161312:0.219373:0.170298:0.219373:0.170298:0.204459:0.161312:0.204459:0.000000
y solo si   no es invertible, :@0.080973:0.234502:0.256116:0.234502:0.256116:0.219563:0.080973:0.219563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.135927:0.234502:0.144913:0.234502:0.144913:0.219588:0.135927:0.219588:0.000000
y que   es no singular si y :@0.080956:0.249631:0.253030:0.249631:0.253030:0.234691:0.080956:0.234691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.121285:0.249631:0.130271:0.249631:0.130271:0.234717:0.121285:0.234717:0.000000
solo si   es invertible.:@0.080956:0.264760:0.220222:0.264760:0.220222:0.249820:0.080956:0.249820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.125033:0.264760:0.134019:0.264760:0.134019:0.249846:0.125033:0.249846:0.000000
La potencia de :@0.080956:0.279889:0.182238:0.279889:0.182238:0.264949:0.080956:0.264949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matrices cumple con :@0.080956:0.295018:0.223873:0.295018:0.223873:0.280078:0.080956:0.280078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las propiedades de los :@0.080956:0.310147:0.231405:0.310147:0.231405:0.295207:0.080956:0.295207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponentes.:@0.080956:0.325276:0.161919:0.325276:0.161919:0.310336:0.080956:0.310336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Sea     :@0.080995:0.340405:0.154922:0.340405:0.154922:0.325465:0.080995:0.325465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.126893:0.340405:0.135879:0.340405:0.135879:0.325490:0.126893:0.325490:0.000000
∈:@0.139410:0.340027:0.151341:0.340027:0.151341:0.324583:0.139410:0.324583:0.000000
M:@0.154855:0.340405:0.167473:0.340405:0.167473:0.325490:0.154855:0.325490:0.000000
2×2:@0.167411:0.343289:0.182670:0.343289:0.182670:0.334579:0.167411:0.334579:0.000000:0.000000:0.000000
 [ ] con :@0.182619:0.340405:0.239397:0.340405:0.239397:0.325465:0.182619:0.325465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.190568:0.340934:0.202650:0.340934:0.202650:0.324885:0.190568:0.324885:0.000000
A:@0.099971:0.355534:0.108957:0.355534:0.108957:0.340619:0.099971:0.340619:0.000000
 ≠ 0. :@0.108890:0.355534:0.140634:0.355534:0.140634:0.340594:0.108890:0.340594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo  ,     N, :@0.099954:0.370663:0.230997:0.370663:0.230997:0.355723:0.099954:0.355723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.166555:0.370663:0.194835:0.370663:0.194835:0.355748:0.166555:0.355748:0.000000:0.000000:0.000000
∈:@0.198366:0.370285:0.210297:0.370285:0.210297:0.354840:0.198366:0.354840:0.000000
A A:@0.099937:0.385792:0.125827:0.385792:0.125827:0.370877:0.099937:0.370877:0.000000:0.000000:0.000000
m n:@0.108894:0.380279:0.130996:0.380279:0.130996:0.371569:0.108894:0.371569:0.000000:0.000000:0.000000
 = :@0.130953:0.385792:0.148122:0.385792:0.148122:0.370852:0.130953:0.370852:0.000000:0.000000:0.000000
A:@0.148038:0.385792:0.157025:0.385792:0.157025:0.370877:0.148038:0.370877:0.000000
m+n:@0.156961:0.380279:0.175917:0.380279:0.175917:0.371569:0.156961:0.371569:0.000000:0.000000:0.000000
.:@0.175867:0.385792:0.178779:0.385792:0.178779:0.370852:0.175867:0.370852:0.000000
(:@0.099962:0.400921:0.104397:0.400921:0.104397:0.385981:0.099962:0.385981:0.000000
A:@0.104330:0.400921:0.113316:0.400921:0.113316:0.386006:0.104330:0.386006:0.000000
m n:@0.113255:0.395408:0.130793:0.395408:0.130793:0.386698:0.113255:0.386698:0.000000:0.000000:0.000000
)  = :@0.121202:0.400921:0.147919:0.400921:0.147919:0.385981:0.121202:0.385981:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.147835:0.400921:0.156821:0.400921:0.156821:0.386006:0.147835:0.386006:0.000000
mn:@0.156759:0.395408:0.169939:0.395408:0.169939:0.386698:0.156759:0.386698:0.000000:0.000000
.:@0.169891:0.400921:0.172803:0.400921:0.172803:0.385981:0.169891:0.385981:0.000000
•  Si     :@0.080995:0.416050:0.142707:0.416050:0.142707:0.401110:0.080995:0.401110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.114678:0.416050:0.123664:0.416050:0.123664:0.401135:0.114678:0.401135:0.000000
∈:@0.127194:0.415671:0.139126:0.415671:0.139126:0.400227:0.127194:0.400227:0.000000
M:@0.142640:0.416050:0.155257:0.416050:0.155257:0.401135:0.142640:0.401135:0.000000
2×2:@0.155186:0.418934:0.170444:0.418934:0.170444:0.410224:0.155186:0.410224:0.000000:0.000000:0.000000
 [ ] con   :@0.170393:0.416050:0.239655:0.416050:0.239655:0.401110:0.170393:0.401110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.178342:0.416579:0.190424:0.416579:0.190424:0.400530:0.178342:0.400530:0.000000
A:@0.227004:0.416050:0.235990:0.416050:0.235990:0.401135:0.227004:0.401135:0.000000
invertible, se verifican :@0.099977:0.431179:0.245323:0.431179:0.245323:0.416239:0.099977:0.416239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las propiedades :@0.099977:0.446308:0.207655:0.446308:0.207655:0.431368:0.099977:0.431368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguientes: :@0.099977:0.461436:0.173549:0.461436:0.173549:0.446497:0.099977:0.446497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo  ,     Z, :@0.099977:0.476565:0.230702:0.476565:0.230702:0.461626:0.099977:0.461626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.167917:0.476565:0.196197:0.476565:0.196197:0.461651:0.167917:0.461651:0.000000:0.000000:0.000000
∈:@0.199728:0.476187:0.211659:0.476187:0.211659:0.460743:0.199728:0.460743:0.000000
A A:@0.099961:0.491694:0.125827:0.491694:0.125827:0.476780:0.099961:0.476780:0.000000:0.000000:0.000000
m n:@0.108894:0.486182:0.130996:0.486182:0.130996:0.477472:0.108894:0.477472:0.000000:0.000000:0.000000
 = :@0.130953:0.491694:0.148122:0.491694:0.148122:0.476755:0.130953:0.476755:0.000000:0.000000:0.000000
A:@0.148038:0.491694:0.157025:0.491694:0.157025:0.476780:0.148038:0.476780:0.000000
m+n:@0.156961:0.486182:0.175917:0.486182:0.175917:0.477472:0.156961:0.477472:0.000000:0.000000:0.000000
,:@0.175867:0.491694:0.178779:0.491694:0.178779:0.476755:0.175867:0.476755:0.000000
(:@0.099962:0.506823:0.104397:0.506823:0.104397:0.491883:0.099962:0.491883:0.000000
A:@0.104330:0.506823:0.113316:0.506823:0.113316:0.491909:0.104330:0.491909:0.000000
m n:@0.113255:0.501311:0.130793:0.501311:0.130793:0.492601:0.113255:0.492601:0.000000:0.000000:0.000000
)  = :@0.121202:0.506823:0.147919:0.506823:0.147919:0.491883:0.121202:0.491883:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.147835:0.506823:0.156821:0.506823:0.156821:0.491909:0.147835:0.491909:0.000000
mn:@0.156759:0.501311:0.169939:0.501311:0.169939:0.492601:0.156759:0.492601:0.000000:0.000000
.:@0.169891:0.506823:0.172803:0.506823:0.172803:0.491883:0.169891:0.491883:0.000000
(Ev.) Identifica las características de las matrices especiales:@0.619331:0.971366:0.922932:0.971366:0.922932:0.959414:0.619331:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las potencias de matriz :@0.078581:0.624975:0.237171:0.624975:0.237171:0.610035:0.078581:0.610035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nos permiten modelar :@0.078581:0.640104:0.230074:0.640104:0.230074:0.625164:0.078581:0.625164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cómo cambian las :@0.078581:0.655233:0.202997:0.655233:0.202997:0.640293:0.078581:0.640293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
poblaciones a lo largo del :@0.078581:0.670362:0.251686:0.670362:0.251686:0.655422:0.078581:0.655422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiempo, considerando las :@0.078581:0.685491:0.248456:0.685491:0.248456:0.670551:0.078581:0.670551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interacciones entre las :@0.078581:0.700620:0.229440:0.700620:0.229440:0.685680:0.078581:0.685680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
especies. :@0.078581:0.715749:0.141462:0.715749:0.141462:0.700809:0.078581:0.700809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ilustra la dinámica cíclica :@0.078581:0.840323:0.244758:0.840323:0.244758:0.825383:0.078581:0.825383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre depredadores y :@0.078581:0.855452:0.223913:0.855452:0.223913:0.840512:0.078581:0.840512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presas, donde un aumento :@0.078581:0.870581:0.259889:0.870581:0.259889:0.855641:0.078581:0.855641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la población de presas :@0.078581:0.885710:0.250279:0.885710:0.250279:0.870770:0.078581:0.870770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conduce a un aumento :@0.078581:0.900839:0.237563:0.900839:0.237563:0.885899:0.078581:0.885899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la población de :@0.078581:0.915968:0.204905:0.915968:0.204905:0.901028:0.078581:0.901028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
depredadores, y viceversa.:@0.078581:0.931097:0.251387:0.931097:0.251387:0.916157:0.078581:0.916157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078581:0.560365:0.244955:0.560365:0.244955:0.543418:0.078581:0.543418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemáticas y :@0.078581:0.577006:0.187574:0.577006:0.187574:0.560573:0.078581:0.560573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biología:@0.078581:0.593648:0.137624:0.593648:0.137624:0.577214:0.078581:0.577214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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