{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 1 " " }{TEXT 256 40 "INTRODUCCION AL ALGEBRA LINE AL EN MAPLE:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 " " 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have b een redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r %.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRdecompG%*Wr onskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG%(backsubG %%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%)choleskyG %$colG%'coldimG%)colspaceG%(colspanG%*companionG%'concatG%%condG%)copy intoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delrowsG%$detG%%diagG%( divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+eigenvect sG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffgausselimG%*fibonac ciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqnsG%*genmat rixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransposeG%)ihe rmiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG%*issimila rG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsqrsG%)lins olveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)multiplyG %%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG%*potentia lG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG%)rowspace G%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackmatrixG%*s ubmatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvesterG%)toep litzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG%'vectorG %*wronskianG" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Generacion de ma trices:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "A:=array(1..4,1.. 5,[[1,4,2,6,7],[x,exp(1),y,Pi,z],[a,b,c,d,e],[28/7,3+2*I,5^2,23,1/10]] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7'\"\"\"\"\" %\"\"#\"\"'\"\"(7'%\"xG-%$expG6#F*%\"yG%#PiG%\"zG7'%\"aG%\"bG%\"cG%\"d G%\"eG7'F+^$\"\"$F,\"#D\"#B#F*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "B:=array([[1,4,2,6,7],[x,exp(1),y,Pi,z],[a,b,c,d,e],[ 28/7,3+2*I,5^2,23,1/10]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-% 'matrixG6#7&7'\"\"\"\"\"%\"\"#\"\"'\"\"(7'%\"xG-%$expG6#F*%\"yG%#PiG% \"zG7'%\"aG%\"bG%\"cG%\"dG%\"eG7'F+^$\"\"$F,\"#D\"#B#F*\"#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A[2,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A[2 ,2]; A[3,5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"eG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalb(A[2,2]=A[3,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalb(A[1 ,2]=A[4,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'symbolG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "type(A,array);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "type(A,symbol);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "A:=matrix(4,5,[1,4,2,6,7,x,exp(1),y,Pi,z,a,b,c,d,e,28/7,3+2*I,5^2,23, 1/10]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7'\"\" \"\"\"%\"\"#\"\"'\"\"(7'%\"xG-%$expG6#F*%\"yG%#PiG%\"zG7'%\"aG%\"bG%\" cG%\"dG%\"eG7'F+^$\"\"$F,\"#D\"#B#F*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'sym bolG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "type(A,array);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "type(A,matrix);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%% trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?matrix;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "B:=matrix([[1,4,2,6,7],[x,ex p(1),y,Pi,z],[a,b,c,d,e],[28/7,3+2*I,5^2,23,1/10]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7'\"\"\"\"\"%\"\"#\"\"'\"\"(7'% \"xG-%$expG6#F*%\"yG%#PiG%\"zG7'%\"aG%\"bG%\"cG%\"dG%\"eG7'F+^$\"\"$F, \"#D\"#B#F*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=(i,j) ->i+j;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"iG%\"jG6\"6$%)o peratorG%&arrowGF),&9$\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A_f:=matrix(6,3,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$A_fG-%'matrixG6#7(7%\"\"#\"\"$\"\"%7%F+F,\"\"&7%F,F.\"\"'7%F.F0\" \"(7%F0F2\"\")7%F2F4\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A_f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$A_fG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "print(A_f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7(7%\"\"#\"\"$\"\"%7%F)F*\"\"&7%F*F,\"\"'7%F,F.\"\"(7%F.F 0\"\")7%F0F2\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "op(A_f) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7(7%\"\"#\"\"$\"\"%7% F)F*\"\"&7%F*F,\"\"'7%F,F.\"\"(7%F.F0\"\")7%F0F2\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "array(identity,1..2,1..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"\"\"\"!F)7%F)F(F) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Id:=array(identity,1..2 ,1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IdG-%&arrayG6&%)identity G;\"\"\"\"\"#;F*\"\"$7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(Id);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"\" \"\"!F)7%F)F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diag(1,2 ,3,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F )F)7&F)\"\"#F)F)7&F)F)\"\"$F)7&F)F)F)\"\"%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "randmatrix(2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7$7%\"#z\"#c\"#\\7%\"#j\"#d!#f" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Operacio nes con matrices:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A:=matr ix(2,3,[[x,exp(1),Pi],[1,4,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"AG-%'matrixG6#7$7%%\"xG-%$expG6#\"\"\"%#PiG7%F.\"\"%\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "B:=matrix(2,3,[[3+2/5,23,1/1 0],[a,b,c]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7$7 %#\"#<\"\"&\"#B#\"\"\"\"#57%%\"aG%\"bG%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "matadd(A,B,1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'matrixG6#7$7%,&%\"xG\"\"\"#\"#M\"\"&F*,&-%$expG6#F*F*\"#YF*,&%#Pi GF*#F*F-F*7%,&F*F**&\"\"#F*%\"aGF*F*,&\"\"%F**&F9F*%\"bGF*F*,&F9F**&F9 F*%\"cGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(1*A+2* B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%,&%\"xG\"\"\"# \"#M\"\"&F*,&-%$expG6#F*F*\"#YF*,&%#PiGF*#F*F-F*7%,&F*F**&\"\"#F*%\"aG F*F*,&\"\"%F**&F9F*%\"bGF*F*,&F9F**&F9F*%\"cGF*F*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "multiply(A,B);" }}{PARA 8 "" 1 "" {TEXT -1 71 "Error, (in multiply) non matching dimensions for vector/matrix pro duct\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "C:=matrix(3,3,[[1 ,4,2],[17,6,4],[5,8,6]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%' matrixG6#7%7%\"\"\"\"\"%\"\"#7%\"#<\"\"'F+7%\"\"&\"\")F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "multiply(A,C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%,(%\"xG\"\"\"*&\"# " 0 "" {MPLTEXT 1 0 12 "evalm(A&*C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'ma trixG6#7$7%,(%\"xG\"\"\"*&\"# " 0 "" {MPLTEXT 1 0 11 "evalm(A*C); " }}{PARA 8 "" 1 "" {TEXT -1 80 "Error, (in evalm/evaluate) use the &* operator for matrix/vector multiplication\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);" }}{PARA 8 "" 1 "" {TEXT -1 46 "Erro r, (in inverse) expecting a square matrix\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' matrixG6#7%7%#!\"\"\"#G#\"\"\"\"#9F(7%#\"#T\"#c#F,F*#!#:F17%#!#`F1#!\" $F*#\"#JF1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(C^(-1)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%#!\"\"\"#G#\"\"\" \"#9F(7%#\"#T\"#c#F,F*#!#:F17%#!#`F1#!\"$F*#\"#JF1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(C^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"#z\"#W\"#I7%\"$R\"\"$O\"\"##)7%\"$r\"\"$;\"\"# y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "exponential(matrix(2,2 ,[[1,4],[2,3]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$, &-%$expG6#!\"\"#\"\"#\"\"$*&#\"\"\"F/F2-F*6#\"\"&F2F2,&F3F-*&#F.F/F2F) F2F,7$,&F3F1*&#F2F/F2F)F2F,,&F)F1*&F-F2F3F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Comand os basicos:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(C);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!$7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rank(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "transpose(A);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7$%\"xG\"\"\"7$-%$expG6#F)\"\"%7$% #PiG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "adjoint(C);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"%!\")F(7%!##)!\"% \"#I7%\"$1\"\"#7!#i" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "adj(C );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"%!\")F(7%!## )!\"%\"#I7%\"$1\"\"#7!#i" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "multiply(C,adj(C));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7% 7%!$7\"\"\"!F)7%F)F(F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "minor(A,2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7 #7$%\"xG-%$expG6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " submatrix(A,1..2,2..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6 #7$7$-%$expG6#\"\"\"%#PiG7$\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrix G6#7$7%%\"xG-%$expG6#\"\"\"%#PiG7%F,\"\"%\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "submatrix(A,[1,2],[1,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$%\"xG%#PiG7$\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"aG%\"bG%\"cG7%\"\"!,$*&,&F(\"$:\"*& \"#<\"\"\"F)F3!\"\"F3F(F4#F3\"\"&,$*&,&F(F3*&\"#MF3F*F3F4F3F(F4#F3\"#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gausselim(B,r,d);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"aG%\"bG%\"cG7%\"\"! ,$*&,&F(\"$:\"*&\"#<\"\"\"F)F3!\"\"F3F(F4#F3\"\"&,$*&,&F(F3*&\"#MF3F*F 3F4F3F(F4#F3\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "r:='r'; d:='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "print(r); print(d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"rG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%\"dG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ffgausselim(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% 'matrixG6#7$7%%\"aG%\"bG%\"cG7%\"\"!,&F(\"#B*&#\"#<\"\"&\"\"\"F)F3!\" \",&F(#F3\"#5*&#F1F2F3F*F3F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 32 "Sistemas de ecuaciones lineales:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "solve(\{3*x+2* y+2*z+t=2,x+4*y+z+3*t=1,x+y+z+t=2,x+y+z+2*t=2\},\{x,y,z,t\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"tG\"\"!/%\"xG!\"#/%\"zG#\"#8\"\" $/%\"yG#!\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "solve(\{ 3*x+2*y+2*z+t=2,x+4*y+z+3*t=1,x+y+z+t=2,x+y+z+2*t=2\});" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<&/%\"tG\"\"!/%\"xG!\"#/%\"zG#\"#8\"\"$/%\"yG#! \"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG-%$expG6#\"\"\"%# PiG7%F,\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "linsol ve(matrix([[1,2],[1,3]]),matrix([[1,1],[-2,1]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"(\"\"\"7$!\"$\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "genmatrix(\{3*x+2*y+2*z+t=2,x+4*y+z +3*t=1,x+y+z+t=2,x+y+z+2*t=2\},\{x,y,z,t\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"$\"\"#\"\"\"F)7&F*\"\"%F(F*7&F*F*F* F*7&F*F*F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "genmatrix( \{3*x+2*y+2*z+t=2,x+4*y+z+3*t=1,x+y+z+t=2,x+y+z+2*t=2\},\{x,y,z,t\},fl ag);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7'\"\"$\"\"#\"\" \"F)F)7'F*\"\"%F(F*F*7'F*F*F*F*F)7'F*F*F)F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "geneqns(matrix([[1,2],[1,3]]),[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/,&%\"xG\"\"\"*&\"\"#F'%\"yGF'F'\"\"!/,&F& F'*&\"\"$F'F*F'F'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{SECT 1 {PARA 3 "" 0 "" {TEXT -1 28 "Otros comandos interesantes:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "delrows(A,1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7#7%\"\"\"\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG-%$expG6#\"\"\"%#PiG7%F,\"\"%\"\"# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "delcols(A,2..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7#%\"xG7#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "row(A,2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%'vectorG6#7%\"\"\"\"\"%\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "col(A,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% 'vectorG6#7$%\"xG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " row(A,1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'vectorG6#7%%\"xG-%$ expG6#\"\"\"%#PiG-F$6#7%F+\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "col(A,1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'ve ctorG6#7$%\"xG\"\"\"-F$6#7$-%$expG6#F(\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "addcol(A,1,3,1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG-%$expG6#\"\"\",&F(#F,\"\"#%#PiGF,7%F,\"\"% #\"\"&F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG-%$expG6#\"\"\"%# PiG7%F,\"\"%\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "mulcol (A,2,1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG,$- %$expG6#\"\"\"#F-\"\"#%#PiG7%F-F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "augment(matrix([[1,2,3],[4,5,6]]),matrix([[7,8,9],[10 ,11,12]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7(\"\"\" \"\"#\"\"$\"\"(\"\")\"\"*7(\"\"%\"\"&\"\"'\"#5\"#6\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "stackmatrix(matrix([[1,2,3],[4,5,6] ]),matrix([[7,8,9],[10,11,12]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'matrixG6#7&7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'7%\"\"(\"\")\"\"*7%\"# 5\"#6\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "swapcol(A,1,2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%-%$expG6#\"\"\"% \"xG%#PiG7%\"\"%F+\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Generacion de vectores:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "v:=vector([1,2,3,4]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6#7&\"\"\"\"\"#\"\"$\" \"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "vector(4,[1,2,3,4]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"\"\"\"#\"\"$\"\" %" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "v[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " g:=i->i^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"iG6\"6$%)op eratorG%&arrowGF(*$)9$\"\"#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "vector(5,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'ve ctorG6#7'\"\"\"\"\"%\"\"*\"#;\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "randvector(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' vectorG6#7(\"#X!\")!#$*\"##*\"#V!#i" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Operaciones con vectores:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "u:=vector( [4,3,2,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG-%'vectorG6#7&\" \"%\"\"$\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "mata dd(u,v,2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"#6\"#7 \"#8\"#9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(2*u+3*v); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"#6\"#7\"#8\"#9" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 6 "Bases:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "triv ial:=\{\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(trivialG<\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "v1:=vector([1,0,0]):\nv2:=v ector([0,1,0]):\nv3:=vector([0,0,1]):\nv4:=vector([1,1,1]):\nbasis(\{v 1,v2,v3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%%#v1G%#v2G%#v3G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "basis(\{v1,v2,v3,v4\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%%#v1G%#v2G%#v3G" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 9 "print(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'matrixG6#7%7%\"\"\"\"\"%\"\"#7%\"#<\"\"'F)7%\"\"&\"\")F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "rowspace(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'vectorG6#7%\"\"\"\"\"!F)-F%6#7%F)F(F)-F%6#7%F )F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "rowspan(C);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'vectorG6#7%\"\"!!#i!#I-F%6#7%\"\" \"\"\"%\"\"#-F%6#7%F(F(!$7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 42 "Subespacio suma y sube spacio intersecci\363n:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "s umbasis(\{v1,v2\},\{v3,v4\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%%#v 1G%#v2G%#v3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "intbasis(\{ v1,v2\},\{v3,v4\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#-%'vectorG6#7 %\"\"\"F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "N\372cleo e imagen:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "kernel(C,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print( d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "d:='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "kernel(A,d);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<#-%'vectorG6#7%,$*&,&%#PiG!\"#-%$expG 6#\"\"\"F0F0,&%\"xGF,F+F0!\"\"\"\"#F0,$*&F1F3,&F2!\"%F-F0F0F3" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(d);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "d :='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "colspace(C,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%-%'vectorG6#7%\"\"\"\"\"!F)-F%6#7%F)F(F)-F%6#7%F)F)F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(d);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "d:='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 35 "Polinomios caracteristico y minimo:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 54 "M:=matrix([[2,1,0,0],[0,2,0,0],[0,0,1,1],[0,0,-2,4] ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7&7&\"\"#\"\" \"\"\"!F,7&F,F*F,F,7&F,F,F+F+7&F,F,!\"#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "charpoly(M,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#*&),&%\"tG\"\"\"\"\"#!\"\"F(F',(*$)F&F(F'F'*&\"\"&F'F&F'F)\"\"'F'F' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "charpoly(matrix([[a,exp (1)],[2+3*I,1/10]]),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$)%\"tG \"\"#\"\"\"F(*&#F(\"#5F(F&F(!\"\"*&%\"aGF(F&F(F,*&#F(F+F(F.F(F(*&F'F(- %$expG6#F(F(F,*&^#!\"$F(F2F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "minpoly(M,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*!#7\"\"\"*& \"#;F%%\"tGF%F%*&\"\"(F%)F(\"\"#F%!\"\"*$)F(\"\"$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "minpoly(matrix([[a,exp(1)],[2+3*I,1 /10]]),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,-%$expG6#\"\"\"!\"#*&^ #!\"$F'F$F'F'*&#F'\"#5F'%\"aGF'F'*&,&#!\"\"F.F'F/F3F'%\"tGF'F'*$)F4\" \"#F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Autovalores:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\" $\"\"#F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Autovectores:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "eigenvects(M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7 %\"\"#\"\"$<$-%'vectorG6#7&\"\"\"\"\"!F,F,-F(6#7&F,F,F+F+7%F%F+<#-F(6# 7&F,F,F+F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 43 "Diagonalizacion y forma canonica de Jorda n:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "jordan(M,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"$\"\"!F)F)7&F)\"\"#\"\" \"F)7&F)F)F+F)7&F)F)F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 " print(P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"!\"\" \"F(!\"$7&F(F(F)F(7&!\"\"F(\"\"#\"\"%7&!\"#F(F.F/" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 7 "P:='P';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"PGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }