{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 "" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 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 "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 "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 "Times" 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 "Nor mal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 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 "" {TEXT 256 49 "M\351todos diretos para s olu\347\343o de sistemas lineares" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 257 46 "Implementa\347\343o do m\351todo de elim ina\347\343o de Gauss" }}{PARA 0 "" 0 "" {TEXT -1 68 "s\343o incluidos um procedimento para o m\351todo de elimina\347\343o de Gauss " } {TEXT 258 12 "triangGauss " }{TEXT -1 11 "e um outro " }{TEXT 261 14 " pvtriangGauss " }{TEXT -1 55 "para dito m\351todo com estrat\352gia de pivotamento parcial." }{TEXT 259 3 ". " }{TEXT -1 220 "Ambos os proc edimentos recebem como argumentos uma matriz quadrada A de tamanho nxn , um vetor de constantes b de tamanho n e o pr\363prio n. No primeiro procedimento s\343o realizadas verifica\347\365es de n\343o nulidade \+ dos piv\364s. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 39 "Implementa\347\343o do m\351todo de fatora\347\343o LU" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "Incluem -se dois procedimentos desenvolvidos para o m\351todo de fatora\347ao \+ LU. Um destes, " }{TEXT 262 13 "fatoracaoLU, " }{TEXT -1 68 " n\343o realiza pivotamento e n\343o verifica nulidade dos pivos. O outro " } {TEXT 263 13 "pvfatoracaoLU" }{TEXT -1 29 " realiza pivotamento parcia l." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Os \+ procedimentos com estrat\352gia de pivotamento parcial utilizam o proc edimento " }{TEXT 264 12 "intercambiar" }{TEXT -1 212 " que permite in tercambiar filas do sistema. Mas esto n\343o \351 essencial e um bom \+ exerc\355cio \351 o de eliminar o interc\342mbio expl\355cito de filha s e utilizar um vetor de indices de filhas para indicar ditos interc \342mbios." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 553 "triangGauss := proc(Ain,bin,n) x := vector(n); A : = Ain; b := bin; print(evalm(A),convert(b,Vector[column]));for i from \+ 1 to n-1 do for j from i+1 to n do mult := A[j,i]/A[i,i]; A[j,i] := 0 ; for k from i+1 to n do A[j,k]:= A[j,k]-mult * A[i,k]; end do; b[j]:= b[j]-b[i]*mult; print(evalm(A), convert(b,Vector[column])); end do; e nd do; print(evalm(A),convert(b,Vector[column])); for i from n by -1 \+ to 1 do x[i]:= b[i]; for k from i+1 to n do x[i] := x[i] - x[k]*A[i,k ]; end do; x[i] := x[i]/A[i,i]; print(convert(x,Vector[column])); end \+ do; end proc;" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `x` is implicit ly declared local to procedure `triangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `A` is implicitly declared local to procedure `t riangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `b` is implicit ly declared local to procedure `triangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `i` is implicitly declared local to procedure `t riangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `j` is implicit ly declared local to procedure `triangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 72 "Warning, `mult` is implicitly declared local to procedure `triangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `k` is impli citly declared local to procedure `triangGauss`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%,triangGaussGf*6%%$AinG%$binG%\"nG6)%\"xG%\"AG%\"bG% \"iG%\"jG%%multG%\"kG6\"F2C)>8$-%'vectorG6#9&>8%9$>8&9%-%&printG6$-%&e valmG6#F;-%(convertG6$F>&%'VectorG6#%'columnG?(8'\"\"\"FO,&F9FOFO!\"\" %%trueG?(8(,&FNFOFOFOFOF9FRC'>8)*&&F;6$FTFNFO&F;6$FNFNFQ>FZ\"\"!?(8*FU FOF9FR>&F;6$FTF[o,&F]oFO*&FXFO&F;6$FNF[oFOFQ>&F>6#FT,&FdoFO*&&F>6#FNFO FXFOFQF@F@?(FNF9FQFOFRC&>&F5FioFho?(F[oFUFOF9FR>F]p,&F]pFO*&&F56#F[oFO FaoFOFQ>F]p*&F]pFOFfnFQ-FA6#-FG6$F5FIF2F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "intercambiar := proc(A,i,j,n); A1:=A; for k from \+ 1 to n do aux := A1[i,k]; A1[i,k]:=A1[j,k]; A1[j,k]:=aux; end do; retu rn A1; end proc; " }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `A1` is imp licitly declared local to procedure `intercambiar`\n" }}{PARA 7 "" 1 " " {TEXT -1 70 "Warning, `k` is implicitly declared local to procedure \+ `intercambiar`\n" }}{PARA 7 "" 1 "" {TEXT -1 72 "Warning, `aux` is imp licitly declared local to procedure `intercambiar`\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-intercambiarGf*6&%\"AG%\"iG%\"jG%\"nG6%%#A1G%\"kG %$auxG6\"F/C%>8$9$?(8%\"\"\"F69'%%trueGC%>8&&F26$9%F5>F<&F26$9&F5>F@F; OF2F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 789 "pvtriangGauss := proc(Ain,bin,n) x := vector(n); A := Ain; b := bin; print(evalm(A) ,evalm(convert(convert(b,Vector[column]),Matrix))); for i from 1 to n- 1 do maior:=i; for l from i+1 to n do if abs(A[maior,i]) < abs(A[l,i ]) then maior := l; end if; end do; if maior <> i then A := intercamb iar(A,i,maior,n); aux:=b[i]; b[i]:=b[maior]; b[maior]:=aux; end if; \+ for j from i+1 to n do mult := A[j,i]/A[i,i]; A[j,i] := 0; for k from i+1 to n do A[j,k]:= A[j,k]-mult * A[i,k]; end do; b[j]:=b[j]-b[i]*mu lt; end do; print(evalm(A), evalm(convert(convert(b,Vector[column]), Matrix))); end do; for i from n by -1 to 1 do x[i]:= b[i]; for k fro m i+1 to n do x[i] := x[i] - x[k]*A[i,k]; end do; x[i] := x[i]/A[i,i]; end do; print(evalm(convert(convert(x,Vector[column]),Matrix))); end proc;" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `x` is implicitly decl ared local to procedure `pvtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `A` is implicitly declared local to procedure `pvtriangGa uss`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `b` is implicitly decl ared local to procedure `pvtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `i` is implicitly declared local to procedure `pvtriangGa uss`\n" }}{PARA 7 "" 1 "" {TEXT -1 75 "Warning, `maior` is implicitly \+ declared local to procedure `pvtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `l` is implicitly declared local to procedure `p vtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 73 "Warning, `aux` is impl icitly declared local to procedure `pvtriangGauss`\n" }}{PARA 7 "" 1 " " {TEXT -1 71 "Warning, `j` is implicitly declared local to procedure \+ `pvtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 74 "Warning, `mult` is i mplicitly declared local to procedure `pvtriangGauss`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `k` is implicitly declared local to procedu re `pvtriangGauss`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%.pvtriangGau ssGf*6%%$AinG%$binG%\"nG6,%\"xG%\"AG%\"bG%\"iG%&maiorG%\"lG%$auxG%\"jG %%multG%\"kG6\"F5C)>8$-%'vectorG6#9&>8%9$>8&9%-%&printG6$-%&evalmG6#F> -FG6#-%(convertG6$-FL6$FA&%'VectorG6#%'columnG%'MatrixG?(8'\"\"\"FW,&F 8(FV?(8),&FVFWFWFWFWF6$FgnFV-F^o 6#&F>6$FinFV>FgnFin@$0FgnFVC&>F>-%-intercambiarG6&F>FVFgnF<>8*&FA6#FV> F`p&FA6#Fgn>FcpF_p?(8+FjnFWF8,*&&F>6$FgpFVFW&F>6$FVFVFY>F\\q\"\" !?(8-FjnFWF&F>6$FgpFcq,&FeqFW*&FjpFW&F>6$FVFcqFWFY>&FA6#Fgp,&F\\rF W*&F`pFWFjpFWFYFC?(FVF&F8FapF`p?(FcqFjnFWFFcr,&FcrFW*&&F 86#FcqFWFiqFWFY>Fcr*&FcrFWF^qFY-FD6#-FG6#-FL6$-FL6$F8FPFTF5F5F5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 737 "fatoracaoLU := proc(Ain,bin ,n) y := vector(n); x:= vector(n); A := Ain; b:=bin; print(`Calculo do s fatores L e U`); print(evalm(A));for i from 1 to n-1 do for j from \+ i+1 to n do A[j,i]:= A[j,i]/A[i,i]; A[j,i]; for k from i+1 to n do A[j ,k]:= A[j,k]-A[j,i] * A[i,k]; end do; end do; print(evalm(A)); end d o; print(`Solucao do sistema L y = b`); for i from 1 to n do y[i]:= b [i]; for j from 1 to i-1 do y[i] := y[i] - A[i,j]*y[j] end do; end do; print(evalm(convert(convert(y,Vector[column]),Matrix))); print(`Soluc ao do sistema U x = y`); for i from n by -1 to 1 do x[i] := y[i]; for \+ j from i+1 to n do x[i] := x[i] - A[i,j]*x[j]; end do; x[i]:= x[i]/A[i ,i]; end do; print(evalm(convert(convert(x,Vector[column]),Matrix))); end proc;" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `y` is implicitly \+ declared local to procedure `fatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `x` is implicitly declared local to procedure `fatorac aoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `A` is implicitly dec lared local to procedure `fatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `b` is implicitly declared local to procedure `fatoracaoL U`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `i` is implicitly declar ed local to procedure `fatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 69 " Warning, `j` is implicitly declared local to procedure `fatoracaoLU`\n " }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, `k` is implicitly declared l ocal to procedure `fatoracaoLU`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#> %,fatoracaoLUGf*6%%$AinG%$binG%\"nG6)%\"yG%\"xG%\"AG%\"bG%\"iG%\"jG%\" kG6\"F2C/>8$-%'vectorG6#9&>8%F6>8&9$>8'9%-%&printG6#%:Calculo~dos~fato res~L~e~UG-FC6#-%&evalmG6#F=?(8(\"\"\"FM,&F9FMFM!\"\"%%trueGC$?(8),&FL FMFMFMFMF9FPC%>&F=6$FSFL*&FWFM&F=6$FLFLFOFW?(8*FTFMF9FP>&F=6$FSFgn,&Fi nFM*&FWFM&F=6$FLFgnFMFOFF-FC6#%;Solucao~do~sistema~L~y~=~bG?(FLFMFMF9F PC$>&F56#FL&F@Ffo?(FSFMFM,&FLFMFMFOFP>Feo,&FeoFM*&&F=6$FLFSFM&F56#FSFM FO-FC6#-FI6#-%(convertG6$-Ffp6$F5&%'VectorG6#%'columnG%'MatrixG-FC6#%; Solucao~do~sistema~U~x~=~yG?(FLF9FOFMFPC%>&F;FfoFeo?(FSFTFMF9FP>Feq,&F eqFM*&F]pFM&F;F`pFMFO>Feq*&FeqFMFZFO-FC6#-FI6#-Ffp6$-Ffp6$F;FjpF^qF2F2 F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fatoracaoLU([[3,2,4], [1,1,2],[4,3,2]],[1,2,3],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Calc ulo~dos~fatores~L~e~UG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6# 7%7%\"\"$\"\"#\"\"%7%\"\"\"F,F)7%F*F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$\"\"#\"\"%7%#\"\"\"F(F,#F)F(7%#F*F(F,#!#5F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$\"\"#\"\"%7%# \"\"\"F(F,#F)F(7%#F*F(F-!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Solu cao~do~sistema~L~y~=~bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6 #7%7#\"\"\"7##\"\"&\"\"$7#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;S olucao~do~sistema~U~x~=~yG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matri xG6#7%7#!\"$7#\"\"&7#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 970 "pvfatoracaoLU := proc(Ain,bin,n) y := vector(n); x:= vector(n); A := Ain; b:=bin; print(`Calculo dos fatores L e U com pivotamento parc ial`); print(evalm(A));for i from 1 to n-1 do maior:=i; for l from i +1 to n do if abs(A[maior,i]) < abs(A[l,i]) then maior := l; end if; \+ end do; if maior <> i then A := intercambiar(A,i,maior,n); aux:=b[i]; b[i]:=b[maior]; b[maior]:=aux; end if; for j from i+1 to n do A[j, i]:= A[j,i]/A[i,i]; A[j,i]; for k from i+1 to n do A[j,k]:= A[j,k]-A[j ,i] * A[i,k]; end do; end do; print(evalm(A)); end do; print(`Soluc ao do sistema L y = b\264`); for i from 1 to n do y[i]:= b[i]; for j f rom 1 to i-1 do y[i] := y[i] - A[i,j]*y[j] end do; end do; print(evalm (convert(convert(y,Vector[column]),Matrix))); print(`Solucao do sistem a U x = y`); for i from n by -1 to 1 do x[i] := y[i]; for j from i+1 t o n do x[i] := x[i] - A[i,j]*x[j]; end do; x[i]:= x[i]/A[i,i]; end do; print(evalm(convert(convert(x,Vector[column]),Matrix))); end proc;" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `y` is implicitly declared loc al to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warn ing, `x` is implicitly declared local to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `A` is implicitly declared loc al to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warn ing, `b` is implicitly declared local to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `i` is implicitly declared loc al to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 75 "Warn ing, `maior` is implicitly declared local to procedure `pvfatoracaoLU` \n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `l` is implicitly declared local to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 73 " Warning, `aux` is implicitly declared local to procedure `pvfatoracaoL U`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `j` is implicitly declar ed local to procedure `pvfatoracaoLU`\n" }}{PARA 7 "" 1 "" {TEXT -1 71 "Warning, `k` is implicitly declared local to procedure `pvfatoraca oLU`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%.pvfatoracaoLUGf*6%%$AinG% $binG%\"nG6,%\"yG%\"xG%\"AG%\"bG%\"iG%&maiorG%\"lG%$auxG%\"jG%\"kG6\"F 5C/>8$-%'vectorG6#9&>8%F9>8&9$>8'9%-%&printG6#%RCalculo~dos~fatores~L~ e~U~com~pivotamento~parcialG-FF6#-%&evalmG6#F@?(8(\"\"\"FP,&F8)FO?(8*,&FOFPFPFPFPFFVFX@$0FVFOC&>F@-%-intercambiarG6&F@FOFVF<>8+&FC6#FO>Fio&FC6#FV>F\\ pFho?(8,FYFPF&F@6$F`pFO*&FcpFP&F@6$FOFOFRFcp?(8-FYFPF&F@6$F` pFip,&F[qFP*&FcpFP&F@6$FOFipFPFRFI-FF6#%&F8FjoFio?(F`pFPFP,&FOFPFPFRFS>Fgq,&FgqFP*&&F@6$FOF`pF P&F86#F`pFPFR-FF6#-FL6#-%(convertG6$-Ffr6$F8&%'VectorG6#%'columnG%'Mat rixG-FF6#%;Solucao~do~sistema~U~x~=~yG?(FOF&F>FjoFgq?(F`pFYF PFFes,&FesFP*&F]rFP&F>F`rFPFR>Fes*&FesFPFfpFR-FF6#-FL6#-Ffr6$-Ffr6 $F>FjrF^sF5F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "pvfatora caoLU([[3,2,4],[1,1,2],[4,3,2]],[1,2,3],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%RCalculo~dos~fatores~L~e~U~com~pivotamento~parcialG" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$\"\"#\"\"%7%\"\" \"F,F)7%F*F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\" %\"\"$\"\"#7%#\"\"\"F(F,#F)F*7%#F)F(#!\"\"F(#\"\"&F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"%\"\"$\"\"#7%#\"\"\"F(F,#F)F*7%# F)F(!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 52 "fatoracaoLU ([[3,-4,1],[1,2,2],[4,0,-3]],[9,3,-2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Calculo~dos~fatores~L~e~UG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$!\"%\"\"\"7%F*\"\"#F,7%\"\"%\"\"!! \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$!\"%\"\"\" 7%#F*F(#\"#5F(#\"\"&F(7%#\"\"%F(#\"#;F(#!#8F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$!\"%\"\"\"7%#F*F(#\"#5F(#\"\"&F(7% #\"\"%F(#\"\")F0!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Solucao~do~s istema~L~y~=~bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7#\" \"*7#\"\"!7#!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%;Solucao~do~sistem a~U~x~=~yG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7#\"\"\"7# !\"\"7#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "pvfatoracao LU([[3,-4,1],[1,2,2],[4,0,-3]],[9,3,-2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%RCalculo~dos~fatores~L~e~U~com~pivotamento~parcialG" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"$!\"%\"\"\"7%F*\" \"#F,7%\"\"%\"\"!!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7 %7%\"\"%\"\"!!\"$7%#\"\"\"F(\"\"##\"#6F(7%#\"\"$F(!\"%#\"#8F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"%\"\"!!\"$7%#\"\"$ F(!\"%#\"#8F(7%#\"\"\"F(#!\"\"\"\"##\"#N\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }