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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 256 "" 0 "" {TEXT 276 19 "Pr\341ctica 1. \301lgebra" }}{PARA 
256 "" 0 "" {TEXT -1 4 "2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Antes d
e empezar" }}{PARA 0 "" 0 "" {TEXT -1 13 "Reinicializar" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "y ca
rgar siempre el paquete de \301lgebra Lineal" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }
{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 132 "Aqu\355 puedes ver todos los comandos de \341lgebra line
al que puedes usar ahora. En esta pr\341ctica tendr\341s que jugar con
 algunos de ellos." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Matrices" }
}{PARA 0 "" 0 "" {TEXT -1 99 "\277C\363mo introducir una matriz con Ma
ple? Ah\355 van un par de ejemplos. Seguro que pillas la din\341mica..
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "A:=matrix([[0,1,2,3],[1,2,3,4],[3,2,1,1]]);" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A:=matrix(3,4,[0,
1,2,3,1,2,3,4,3,2,1,1]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "B:=matrix([[10],[0],[4]]);" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "B:=matrix(3,1,[10,0,4]);" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "C:=matrix([[1,0,2
],[0,2,0],[1,1,1]]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "C:=matrix(3,3,[1,0,2,0,2,0,1,1,1]);" }{TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "E:=matrix([[3,-5,2]]);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "E:=matrix(1
,3,[3,-5,2]);" }{TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 36 "
Operaciones elementales con matrices" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 11 "No comment!" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "transpose(A);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(C);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(C);" }{TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rank(A);" }{TEXT -1 0 "" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 95 "Para mu
ltiplicar matrices hay que usar el comando &* y luego hacer evalm (eva
luaci\363n matricial)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "E:=
evalm(C&*A);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 84 "Sumar y multiplicar por un n\372mero es todav
\355a m\341s f\341cil (\241\241 pero no olvides evalm !!)" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(E+A);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(5*A);" }{TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(-C);" }{TEXT -1 0 "
" }}}{PARA 0 "" 0 "" {TEXT -1 39 "Las matrices tambi\351n se pueden \"
juntar\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "concat(A,B);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "concat(A,B,
C);" }{TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 49 " Transfor
maciones elementales por filas con Maple" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "Dada una matriz " }{XPPEDIT 18 0 "
F;" "6#%\"FG" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
64 "F:=matrix([[1,1,1,-1,1],[2,-2,1,2,0],[3,3,3,3,1],[1,0,-3,4,5]]);" 
}}}{PARA 0 "" 0 "" {TEXT -1 100 "los comandos de Maple que corresponde
n a las transformaciones elementales por filas sobre la matriz " }
{XPPEDIT 18 0 "A;" "6#%\"AG" }{TEXT -1 20 " son los siguientes:" }}
{PARA 15 "" 0 "" {TEXT -1 5 "para " }{TEXT 262 22 "intercambiar las fi
las" }{TEXT 259 1 " " }{TEXT 256 1 "i" }{TEXT 263 1 " " }{TEXT 269 1 "
y" }{TEXT 270 1 " " }{TEXT 260 1 "j" }{TEXT 264 1 " " }{TEXT -1 21 "se
 emplea el comando " }{TEXT 265 16 "swaprow(A, i, j)" }{TEXT -1 1 ":" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "swaprow(F,1,2);" }}}{PARA 
15 "" 0 "" {TEXT -1 11 "el comando " }{TEXT 258 15 "mulrow(A, i, k)" }
{TEXT -1 9 " permite " }{TEXT 257 38 "multiplicar una fila i por un n
\372mero k" }{TEXT -1 1 " " }{TEXT 271 18 "(distinto de cero)" }{TEXT 
-1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "mulrow(F,1,24);" 
}}}{PARA 15 "" 0 "" {TEXT -1 5 "para " }{TEXT 266 15 "sumar a la fila
" }{TEXT 272 1 " " }{TEXT 261 1 "j" }{TEXT 267 1 " " }{TEXT 273 38 "la
 fila i multiplicada por un n\372mero k" }{TEXT -1 22 " se emplea el c
omando " }{TEXT 268 18 "addrow(A, i, j, k)" }{TEXT -1 1 ":" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "addrow(F,1,3,-3);" }}}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Escalonar mat
rices" }}{PARA 0 "" 0 "" {TEXT -1 11 "La funci\363n " }{TEXT 274 9 "ga
usselim" }{TEXT -1 41 " reduce una matriz a su forma escalonada:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(F);" }}}{PARA 0 "
" 0 "" {TEXT -1 11 "La funci\363n " }{TEXT 275 9 "gaussjord" }{TEXT 
-1 50 " reduce una matriz a su forma escalonada reducida:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gaussjord(F);" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 
"" {TEXT -1 34 "Resolviendo sistemas de ecuaciones" }}{PARA 0 "" 0 "" 
{TEXT -1 75 "La funci\363n que resuelve de forma directa el sistema de
 ecuaciones lineales " }{XPPEDIT 18 0 "A*x = B;" "6#/*&%\"AG\"\"\"%\"x
GF&%\"BG" }{TEXT -1 4 " es " }{XPPEDIT 18 0 "linsolve(A,B" "6#-%)linso
lveG6$%\"AG%\"BG" }{TEXT -1 169 ". Maple nos da la soluci\363n general
 en funci\363n de par\341metros (asociados a variables libres), aunque
 la forma en la que Maple escribe los par\341metros es un poco extra
\361a ..." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "linsolve(C,B);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "linsolve(A,B);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "G:=concat(A,C);" }}}{EXCHG 
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