{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 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 "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 "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 "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 256 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 "Normal" -1 257 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 }{PSTYLE "Normal" -1 258 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 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#7er%#&xG%$AddG%(AdjointG%3BackwardSubstituteG%+B andMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalFormG%-BilinearFormG%5Cha racteristicMatrixG%9CharacteristicPolynomialG%'ColumnG%0ColumnDimensio nG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatrixG%0ConditionNumberG %/ConstantMatrixG%/ConstantVectorG%%CopyG%2CreatePermutationG%-CrossPr oductG%-DeleteColumnG%*DeleteRowG%,DeterminantG%)DiagonalG%/DiagonalMa trixG%*DimensionG%+DimensionsG%+DotProductG%6EigenConditionNumbersG%,E igenvaluesG%-EigenvectorsG%&EqualG%2ForwardSubstituteG%.FrobeniusFormG %4GaussianEliminationG%2GenerateEquationsG%/GenerateMatrixG%(GenericG% 2GetResultDataTypeG%/GetResultShapeG%5GivensRotationMatrixG%,GramSchmi dtG%-HankelMatrixG%,HermiteFormG%3HermitianTransposeG%/HessenbergFormG %.HilbertMatrixG%2HouseholderMatrixG%/IdentityMatrixG%2IntersectionBas isG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*IsUnitaryG%2JordanBlockMa trixG%+JordanFormG%1KroneckerProductG%(LA_MainG%0LUDecompositionG%-Lea stSquaresG%,LinearSolveG%$MapG%%Map2G%*MatrixAddG%2MatrixExponentialG% /MatrixFunctionG%.MatrixInverseG%5MatrixMatrixMultiplyG%+MatrixNormG%, MatrixPowerG%5MatrixScalarMultiplyG%5MatrixVectorMultiplyG%2MinimalPol ynomialG%&MinorG%(ModularG%)MultiplyG%,NoUserValueG%%NormG%*NormalizeG %*NullSpaceG%3OuterProductMatrixG%*PermanentG%&PivotG%*PopovFormG%0QRD ecompositionG%-RandomMatrixG%-RandomVectorG%%RankG%6RationalCanonicalF ormG%6ReducedRowEchelonFormG%$RowG%-RowDimensionG%-RowOperationG%)RowS paceG%-ScalarMatrixG%/ScalarMultiplyG%-ScalarVectorG%*SchurFormG%/Sing ularValuesG%*SmithFormG%8StronglyConnectedBlocksG%*SubMatrixG%*SubVect orG%)SumBasisG%0SylvesterMatrixG%/ToeplitzMatrixG%&TraceG%*TransposeG% 0TridiagonalFormG%+UnitVectorG%2VandermondeMatrixG%*VectorAddG%,Vector AngleG%5VectorMatrixMultiplyG%+VectorNormG%5VectorScalarMultiplyG%+Zer oMatrixG%+ZeroVectorG%$ZipG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 26 "U m pouco de \301lgebra Linear" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 24 "a) Matriz diagonaliz\341vel" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "# uma matriz 4x4\nA:=Matrix([[-99, -40, \+ -98, 60], [-77, 63, -49, -37], [98, 47, 95, 37], [23, -85, 4, -99]]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\")oh7s-%'MATRIX G6#7&7&!#**!#S!#)*\"#g7&!#x\"#j!#\\!#P7&\"#)*\"#Z\"#&*\"#P7&\"#B!#&)\" \"%F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "sabemos como conseguir autovetores /valores diretamente do Maple" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "l,S:=Eigenvectors(A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "l:=evalf(l);S:=evalf(S);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG -%'RTABLEG6%\"))=[I(-%'MATRIXG6#7&7#^$$\"+lz)Q0\"!\"($!*z*4+K!#=7#^$$ \"*nU@W$!\")$\"+IV4<6!#<7#^$$!+Hmy0UF9$!+'3@aM\"F<7#^$$!+H2tn5F1$\"+Nv F.EF4&%'VectorG6#%'columnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG-% 'RTABLEG6%\")!y'y&)-%'MATRIXG6#7&7&^$$\"+ztS>p!#5$!+kQgeX!#?^$$!+RP?p= !\")$\"+]_C(G\"!#;^$$!+l!onz(!\"*$\"+[[mz@!#<^$$!+v!ok\\\"F?$!+G&zC1)! #>7&^$$!+Q$=R@#F?$\"+z*\\D#=zF47&^$$\"+&[XtF(!#6$\"+bt=CEF4^$$\"+ 5a*zA#F8$!+JYSU:F;^$$\"+L,uehF?$!+O(og$=FB^$$\"+tL(y4'F1$\"+iLKA\")!#@ 7&$\"\"\"\"\"!F`pF`pF`p%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 153 "Sabemos que para matrizes reais, os autovalores devem vir em pare s conjugados. Isso n\343o acontece acima, logo a parte imagin\341ria p arece ser erro num\351rico." }}{PARA 0 "" 0 "" {TEXT -1 75 "Vamos ver, plotando o gr\341fico, se a matriz de fato tem 4 autovalores reais." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "p:=CharacteristicPolynomi al(A,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,,\"(U!H;\"\"\" *$)%'lambdaG\"\"%F'F'*&\"#SF')F*\"\"$F'F'*&\"&W8\"F')F*\"\"#F'!\"\"*& \"'JZVF'F*F'F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p:=unappl y(p,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGf*6#%'lambdaG6\" 6$%)operatorG%&arrowGF(,,\"(U!H;\"\"\"*$)9$\"\"%F.F.*&\"#SF.)F1\"\"$F. F.*&\"&W8\"F.)F1\"\"#F.!\"\"*&\"'JZVF.F1F.F;F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(p(x),x=-120..120);" }}{PARA 13 "" 1 "" {GLPLOT2D 522 316 316 {PLOTDATA 2 "6%-%'CURVESG6$7bo7$$!$?\"\"\"!$\")iJoGF*7$$!3/+++:M%Q<\"! #:$\"37&*oh!)G\\^@!#57$$!3'*******HooZ6F0$\"3EvZZ[$3I^\"F37$$!30++DD\" G\\7\"F0$\"3!)poi&H_w,\"F37$$!3+++]?%p@5\"F0$\"35?OQ.4@_d!#67$$!3)**** **HL!)40\"F0$!30g([UhZCT#FC7$$!3u******4$>X***!#;$!3U;X#ej(o!R)FC7$$!3 M*****\\M%o\"[*FL$!3eM![\"F37$$!3e+++Sd=vpFL$!3^B%) [-EJ98F37$$!3w******HmO:lFL$!3Q5S?I))\\C6F37$$!3w******>#>x*fFL$!37YA( z$o@%z)FC7$$!3q++++j%zZ&FL$!3?Bx)48)RFL$\"3^a v73-cS%*!#77$$!3h+++!)o6BNFL$\"3K@jS<(3gl#FC7$$!3'3++]cH,*HFL$\"3bKOGG 7b:UFC7$$!3p+++![X$=DFL$\"3!*\\%)ek0*f9&FC7$$!3%)*****\\cB2+#FL$\"3js. _[z!ei&FC7$$!3v*****\\4Dy]\"FL$\"3LwK3b6\\>bFC7$$!3s*******\\s`$**!#<$ \"3wSe%GC')*)z%FC7$$!3u))****\\Yg7_Fft$\"3Gf*G8;l>e$FC7$$!37^******\\h %=\"!#=$\"3%*GbEG;Q!o\"FC7$$\"33)*****\\:#H<&Fft$!3k\\=cF#)*3<*Fir7$$ \"3U*)****\\g3z(*Fft$!3_SE_f,^gOFC7$$\"3A,++!*pQv9FL$!3#[$e.p2SyqFC7$$ \"3_******R3L*)>FL$!3ujA#QM*p.6F37$$\"3q+++IY7#\\#FL$!3U/a8UfbC:F37$$ \"3!******\\Z.'yHFL$!3G9-`ti,a>F37$$\"3e)******Gb(=NFL$!3S$>\"H.T!QW#F 37$$\"3J)*****>d5/SFL$!3g]KoF3t#)GF37$$\"3r********3KAXFL$!3>yM*=-%)[L $F37$$\"3!*)****\\(3!>*\\FL$!3AOGq!>:br$F37$$\"3!G+++#eF0bFL$!3%=D\"eD 3c#3%F37$$\"3!)*****\\j@$))fFL$!3%ep)QE(eMO%F37$$\"3T+++lEySiFL$!3CP%f r?,#zWF37$$\"3-,++&pVK\\'FL$!3e05mp71qXF37$$\"3l****\\(\\q+u'FL$!3<5oe C%3@j%F37$$\"3G)******H(*o)pFL$!3sC(*=5M!\\m%F37$$\"3y)**\\Pp*4;rFL$!3 G4LgD\"e%pYF37$$\"3I****\\(3-`C(FL$!3I?.\"[t/[m%F37$$\"3!)***\\7[/XP(F L$!3y1Wzw(>0l%F37$$\"3J+++voq.vFL$!3uo?e-J++vR8sC*FL$!3c!HIV=LC3$F37$$\"3c-++S_9z%*FL$!3Gb(*y0QHqEF3 7$$\"3L-++0`'\\u*FL$!3Fr?Ig`OE@F37$$\"3@+++P&y5+\"F0$!3wO^JX)49]\"F37$ $\"3.++]+Q&[-\"F0$!31)Qu%z9\"zp)FC7$$\"3')*****R1H'[5F0$!3U=Q[k.Ue;FC7 $$\"3-++v`%yR2\"F0$\"3'=[-,Hg^o'FC7$$\"3?++]VyK*4\"F0$\"3w'p*zZ%3Qf\"F 37$$\"3;+++W/fB6F0$\"3/p1T7M))oDF37$$\"37++]WI&y9\"F0$\"3z,GF)okcj$F37 $$\"35+]P$y*)3;\"F0$\"3CrW;B\"=#[UF37$$\"31++DAl#R<\"F0$\"3y$**QTsO\"* )[F37$$\"3-+]7hK'p=\"F0$\"3-x#)*>X%4fbF37$$\"$?\"F*$\")AxeiF*-%'COLOUR G6&%$RGBG$\"*++++\"!\")$F*F*F^bl-%+AXESLABELSG6$%\"xGQ!6\"-%%VIEWG6$;F (Fcal%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "De fato, portant o devemos trabalhar com a parte real" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Lambda:=DiagonalMatrix(Re(l));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'LambdaG-%'RTABLEG6%\")gM4))-%'MATRIXG6#7&7&$\"+lz)Q0 \"!\"(\"\"!F1F17&F1$\"*nU@W$!\")F1F17&F1F1$!+Hmy0UF5F17&F1F1F1$!+H2tn5 F0%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "S:=Re(S);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG-%'RTABLEG6%\")/m5))-%'MATRIXG6# 7&7&$\"+ztS>p!#5$!+RP?p=!\")$!+l!onz(!\"*$!+v!ok\\\"F67&$!+Q$=R@#F6$!+ /&yX@&F6$!+q!)z*[#F6$!+B'Gy%GF07&$\"+&[XtF(!#6$\"+5a*zA#F3$\"+L,uehF6$ \"+tL(y4'F07&$\"\"\"\"\"!FMFMFM%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# conferindo\nA.S=S.Lambda;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%'RTABLEG6%\")k]:))-%'MATRIXG6#7&7&$\"3i++E*=!G#H(!#; $!3d;++.g1MkF/$\"3)****4?Ga\"zK!#:$\"3')**fh[\\#yf\"F47&$!3:+&**R\">AL BF4$!3K7+?i<$\\z\"F/$\"3/++ygf:Z5F4$\"3/***RA>92/$F/7&$\"3M(**\\*Q'3&p w!#<$\"3Q:+?f&y!pwF/$!3-++DqYB!f#F4$!3%))**fM)o)3^'F/7&$\"33+5@&*y)Q0 \"F4$\"3wY++q#H@W$FC$!3%3++8!py0UF/$!3%***H!3tIx1\"F4%'MatrixG-F%6%\") oJ<))-F)6#7&7&$\"3#RHg;;!G#H(F/$!3CUa$*[f1MkF/$\"3[?\">xGa\"zKF4$\"3kw \\k[\\#yf\"F47&$!3A-5\">*=ALBF4$!3a;$ouJK\\z\"F/$\"3a+;y')3^ 'F/7&$\"3)******\\'z)Q0\"F4$\"3'*******pE9UMFC$!3)*******Gmy0UF/$!3-++ +H2tn5F4FS" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 137 "O polin\364mio car acter\355stico manda cada um dos distintos autovalores em zero. Pelo q ue sabemos de c\341lculo funcional, deve ser ent\343o p(A)=0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")w^k%)-%'MATRIXG6#7&7&\"\"!F,F,F,F+F+F+%' MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Note que o Maple sabe \+ calcular polin\364mios de matrizes sem mais delongas. O mesmo n\343o o corre com" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(A);" }} {PARA 8 "" 1 "" {TEXT -1 154 "Error, invalid input: sin expects its 1s t argument, x, to be of type algebraic, but received Matrix(4, 4, [[.. .],[...],[...],[...]], datatype = anything)\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Ok, basta achar q polin\364mio de grau 3 com q(lambda )=sen(lambda) para os autovalores (matriz \351 diagonaliz\341vel)." }} {PARA 0 "" 0 "" {TEXT -1 39 "Isso pode ser feito de v\341rias maneiras :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "q:=unapply(a*x^3+b*x^2 +c*x+d,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qGf*6#%\"xG6\"6$%)op eratorG%&arrowGF(,**&%\"aG\"\"\")9$\"\"$F/F/*&%\"bGF/)F1\"\"#F/F/*&%\" cGF/F1F/F/%\"dGF/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 " lambda1:=Lambda[1,1]:\nlambda2:=Lambda[2,2]:\nlambda3:=Lambda[3,3]:\nl ambda4:=Lambda[4,4]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "eq 1:=q(lambda1)=sin(lambda1);\neq2:=q(lambda2)=sin(lambda2);\neq3:=q(lam bda3)=sin(lambda3);\neq4:=q(lambda4)=sin(lambda4);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$eq1G/,**&$\"+>@`q6!\"$\"\"\"%\"aGF+F+*&$\"+V)z16\" !\"&F+%\"bGF+F+*&$\"+lz)Q0\"!\"(F+%\"cGF+F+%\"dGF+$!+f&=W*)*!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,**&$\"+*yp$yS!\")\"\"\"%\"aGF +F+*&$\"+;Y$[=\"F*F+%\"bGF+F+*&$\"*nU@W$F*F+%\"cGF+F+%\"dGF+$!+FhXgH!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/,**&$\"+^]YRu!\"&\"\"\"% \"aGF+!\"\"*&$\"+%$eq4G/,**&$\"+`_E <7!\"$\"\"\"%\"aGF+!\"\"*&$\"+5*[+9\"!\"&F+%\"bGF+F+*&$\"+H2tn5!\"(F+% \"cGF+F-%\"dGF+$\"+3rd1T!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "# Um modo: solve\nsolve(\{eq1,eq2,eq3,eq4\},\{a,b,c,d\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"aG$\"+1'QCS#!#:/%\"bG$!+C#f&eA!# 9/%\"cG$!+9Jp#>$!#6/%\"dG$!+\"R*yf=!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "assign(%); #isso faz as atribui\347\365es acima: a pa ssa a ser o n\372mero .2402438606e-5 e assim por diante" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "q(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&$\"+1'QCS#!#:\"\"\")%\"xG\"\"$F(F(*&$\"+C#f&eA!#9F()F*\"\"#F (!\"\"*&$\"+9Jp#>$!#6F(F*F(F2$\"+\"R*yf=!#5F2" }}}{EXCHG {PARA 256 "" 1 "" {TEXT -1 142 "Existe a op\347\343o de usar MatrixFunction para ca lcular o seno de A via Maple. Entetanto, no meu computador, o Maple se perdeu fazendo as contas. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "q(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")%=Rk)-%'MAT RIXG6#7&7&$\"3%******H_Bj7$!#<$\"3\"******\\PS?#HF.$\"3*******fV$\"3'****** 4ALS>\"F.$\"3-+++$3QCO\"F.7&$!3'******R4Bdz#F.$!3=+++#\\?XF#F.$!3$**** **pc69/$F.$!33+++P\"*z^HF.7&$!3M+++c.N'R&!#=$\"3%******>ypPG%F:$!3=+++ /!*=SVFK$!3E+++t:A'*[FK%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Podemos tamb\351m armar 4 equa\347\365es em forma matricial: Mz=d. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "unassign('a','b','c','d '); # esquece respostas" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " eq1;eq2;eq3;eq4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**&$\"+>@`q6!\"$ \"\"\"%\"aGF)F)*&$\"+V)z16\"!\"&F)%\"bGF)F)*&$\"+lz)Q0\"!\"(F)%\"cGF)F )%\"dGF)$!+f&=W*)*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**&$\"+*yp$ yS!\")\"\"\"%\"aGF)F)*&$\"+;Y$[=\"F(F)%\"bGF)F)*&$\"*nU@W$F(F)%\"cGF)F )%\"dGF)$!+FhXgH!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**&$\"+^]YRu! \"&\"\"\"%\"aGF)!\"\"*&$\"+ " 0 "" {MPLTEXT 1 0 175 "M:=Matrix(4,4,[1170532.119,11106.79843,105.3887965,1,\n40.783 69789,11.84834616,3.44214267,1,\n-74394.65051,1768.864117,-42.05786629 ,1,\n-1217265.253,11400.48910,-106.7730729,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'RTABLEG6%\")S72%)-%'MATRIXG6#7&7&$\"+>@`q6!\"$ $\"+V)z16\"!\"&$\"+lz)Q0\"!\"(\"\"\"7&$\"+*yp$yS!\")$\"+;Y$[=\"F;$\"*n U@W$F;F77&$!+^]YRuF3$\"+ " 0 "" {MPLTEXT 1 0 70 "d :=Matrix(4,1,[-.9894418559,-.2960456127,.9381202376,.4106577108e-1]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG-%'RTABLEG6%\")o(4f)-%'MATRI XG6#7&7#$!+f&=W*)*!#57#$!+FhXgHF07#$\"+wB?\"Q*F07#$\"+3rd1T!#6%'Matrix G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "LinearSolve(M,d);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")s_k%)-%'MATRIXG6#7&7#$ \"3g?s*fgQCS#!#B7#$!3W8y'RAf&eA!#A7#$!3K\"[@Q6$p#>$!#>7#$!3w5AA\"R*yf= !#=%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "M^(-1).d;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"))e+q)-%'MATRIXG6#7&7#$ \"3=?s*fgQCS#!#B7#$!3W8y'RAf&eA!#A7#$!3K\"[@Q6$p#>$!#>7#$!3w5AA\"R*yf= !#=%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(CurveF itting);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+%3ArrayInterpolationG%(B SplineG%-BSplineCurveG%,InteractiveG%-LeastSquaresG%8PolynomialInterpo lationG%6RationalInterpolationG%'SplineG%4ThieleInterpolationG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "# Se restri\347\365es n\343 o envolvem derivadas, podemos usar\nPolynomialInterpolation([lambda1,l ambda2,lambda3,lambda4],\n[sin(lambda1),sin(lambda2),sin(lambda3),sin( lambda4)],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&$\"+0'QCS#!#:\"\" \")%\"xG\"\"$F(F(*&$\"*Af&eA!#8F()F*\"\"#F(!\"\"*&$\"+9Jp#>$!#6F(F*F(F 2$\"+*Q*yf=!#5F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 28 "b) Matriz n\343o d iagonaliz\341vel" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "A:=Matr ix(3,3,[[-42, 45, 2835], [49, 42, -1323], [0, 0, -63]]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\")!3]!))-%'MATRIXG6#7%7%!#U\" #X\"%NG7%\"#\\\"#U!%B87%\"\"!F6!#j%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "# tentar diagonalizar\nEigenvectors(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\")+Ij%)-%'MATRIXG6#7%7#\"#j7#!# jF-&%'VectorG6#%'columnG-F$6%\")Ozs%)-F(6#7%7%#\"\"$\"\"(#!#:F<\"\"!7% \"\"\"FAF?7%F?F?F?%'MatrixG" }}}{EXCHG {PARA 256 "" 1 "" {TEXT -1 157 "Vemos acima que um suposto autovetor \351 nulo, o que n\343o pode ser por defini\347\343o. A matriz \351 de fato n\343o diagonaliz\341vel e tem autovalores 63 e -63 (esse duplo)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "p:=CharacteristicPolynomial(A,lambda);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"pG,*\"'Z+D!\"\"*$)%'lambdaG\"\"$\"\"\"F,*&\" #jF,)F*\"\"#F,F,*&\"%pRF,F*F,F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p:=unapply(p,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"p Gf*6#%'lambdaG6\"6$%)operatorG%&arrowGF(,*\"'Z+D!\"\"*$)9$\"\"$\"\"\"F 3*&\"#jF3)F1\"\"#F3F3*&\"%pRF3F1F3F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "plot(p(x),x=-80..70);" }}{PARA 13 "" 1 "" {GLPLOT2D 530 305 305 {PLOTDATA 2 "6%-%'CURVESG6$7Y7$$!#!)\"\"!$!&F8%F *7$$!3k++](oUIn(!#;$!3kRBA$fiUj#!#87$$!3I**\\7y)e&)Q(F0$!3$)Qt*H1S?i\" F37$$!3%)***\\73F'oqF0$!3s3NNv*=!)*y!#97$$!3Q++voXdYnF0$!3$=jyLIj=g#F> 7$$!3l+]i:F0EkF0$!3,1]da!z?-#!#:7$$!3V+]7Gz))GhF0$!3(*>Db'\\'4ROFI7$$! 3&***\\7.5>@eF0$!377/ez1))yFF>7$$!3))**\\7./(H]&F0$!3go\\\"3()4z\\(F>7 $$!3i**\\iS.x&=&F0$!33%=*oqs'fU\"F37$$!3m****\\(3\"\\f[F0$!3mQT#=(zm:B F37$$!3')***\\P9/@d%F0$!3#p!o5/;+YKF37$$!3S****\\7Xd[UF0$!3cT\">ap0#RW F37$$!3!*****\\PkrBRF0$!3#*4sXd+0tdF37$$!30++]([b1h$F0$!3;A0$z#[&z;(F3 7$$!38+]7`hOELF0$!3!=,q8f7@^)F37$$!37++]P'=$))HF0$!3kU2D)er'=5!#77$$!3 -+++]![>q#F0$!3K0@E*>!Rl6F[q7$$!3%)**\\7y4$)oBF0$!3y\"**y2$*)oR8F[q7$$ !3E+++Df'R2#F0$!3%G0Qg0Pb\\\"F[q7$$!3s**\\7GAX]F [q7$$!3%=+]i!z(yD)!#<$!3(Qp\"GyZQN@F[q7$$!3g2+]P%QS2&F]s$!3O[Z$R(y;%G# F[q7$$!3U***\\7.Cpw\"F]s$!32Sa*f2H%GCF[q7$$\"3]++D\"yG>6\"F]s$!3VOJm#y 4Qa#F[q7$$\"3'p***\\(oo6A%F]s$!3ciYEF0$!3-lxNS@0GHF[q7$$\"3/,+](Q(zSHF0$!3!QJtPf,&oGF[q7$$\"3X)*\\(=-, FC$F0$!3Gjc0MD2%y#F[q7$$\"3k+]P4tFeNF0$!3?&y'460ckEF[q7$$\"3#*)***\\73 \"o'QF0$!3;972'pU]^#F[q7$$\"3y)*\\(oz;)*=%F0$!3EOcd+m'>K#F[q7$$\"3\\++ +]*44]%F0$!3S#oE*eA\"))4#F[q7$$\"3-,+DJw/>[F0$!3dU*)\\.\"\\4$=F[q7$$\" 3(3+v=(4bM^F0$!3#)37:OC\"Q_\"F[q7$$\"3C,vVt$3&z_F0$!3M'=&3UjKo8F[q7$$ \"3g,++vdYCaF0$!3`l()=nk`.7F[q7$$\"3S+]i:Lg!f&F0$!30t,mo2*H+\"F[q7$$\" 3=***\\i&3ucdF0$!3kDP=Zl3(*yF37$$\"3@+]7`iL0fF0$!3g-%3\\.:$zeF37$$\"3C ,++];$R0'F0$!3!)H')e%)f[bPF37$$\"3C,v$fLlB@'F0$!3?Yi2Y?+s8F37$$\"3E,]( =-*zqjF0$\"3Q]R3jAnO6F37$$\"3,,++v-WAlF0$\"3!3RYl@^sl$F37$$\"3y+]7G:3u mF0$\"3Cw7\")QVz'H'F37$$\"3R+D1k2/PoF0$\"3EN*eOK[$o#*F37$$\"#qF*$\"'BQ 7F*-%'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fb]l-%+AXESLABELSG6$%\"xGQ!6\" -%%VIEWG6$;F(Fg\\l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 200 "No gr\341fico acima, vemos que o polin\364mio caracter\355stico t em derivada nula na raiz -63. Ou seja, p(lambda1)=p(lambda2)=0 e p'(la mbda)=0 para a raiz dupla. Pelo c\341lculo funcional, deve ser ent\343 o p(A)=0. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\")7T\"\\)-%'MATRIXG6#7%7% \"\"!F,F,F+F+%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Vamos c alcular novamente o seno de A." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# nesse exemplo o atalho funciona:\nsinA:=MatrixFunction(A,sin (x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sinAG-%'RTABLEG6%\")?id$ )-%'MATRIXG6#7%7%,$*&#\"\"#\"\"$\"\"\"-%$sinG6#\"#jF3!\"\",$*&#\"\"&\" \"(F3F4F3F3,$*&\"%NGF3-%$cosGF6F3F37%,$*&#F=\"\"*F3F4F3F3,$*&#F1F2F3F4 F3F3,$*&\"%B8F3FAF3F87%\"\"!FO,$F4F8%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Para isso, agora as equa\347\365es s\343o tr\352s e en volvem derivada:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "q:=unap ply(a*x^2+b*x+c,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qGf*6#%\"xG 6\"6$%)operatorG%&arrowGF(,(*&%\"aG\"\"\")9$\"\"#F/F/*&%\"bGF/F1F/F/% \"cGF/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "eq1:=q(63)= sin(63);\neq2:=q(-63)=sin(-63);\neq3:=D(q)(-63)=D(sin)(-63);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,(*&\"%pR\"\"\"%\"aGF)F)*&\"#jF)%\"b GF)F)%\"cGF)-%$sinG6#F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,(* &\"%pR\"\"\"%\"aGF)F)*&\"#jF)%\"bGF)!\"\"%\"cGF),$-%$sinG6#F,F." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/,&*&\"$E\"\"\"\"%\"aGF)!\"\"% \"bGF)-%$cosG6#\"#j" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solv e(\{eq1,eq2,eq3\},\{a,b,c\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/% \"aG,&*&#\"\"\"\"%QzF)-%$sinG6#\"#jF)F)*&#F)\"$E\"F)-%$cosGF-F)!\"\"/% \"bG,$*&#F)F.F)F+F)F)/%\"cG,&*&#F)\"\"#F)F+F)F4*&#F.F?F)F2F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "q(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'RTABLEG6%\")!)y8()-%'MATRIXG6#7%7%,$*&#\"\"#\"\"$\"\"\"-%$sinG6#\"#j F1!\"\",$*&#\"\"&\"\"(F1F2F1F1,$*&\"%NGF1-%$cosGF4F1F17%,$*&#F;\"\"*F1 F2F1F1,$*&#F/F0F1F2F1F1,$*&\"%B8F1F?F1F67%\"\"!FM,$F2F6%'MatrixG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Ok, mesma resposta que o Maple ret ornou." }}{PARA 0 "" 0 "" {TEXT -1 92 "A fun\347\343o PolynomialInterp olation n\343o funciona aqui, pois uma das equa\347\365es envolve deri vadas." }}{PARA 0 "" 0 "" {TEXT -1 90 "O que poder\355amos ter usado \+ \351 dsolve. As condi\347\365es inciais s\343o as equa\347\365es acima e a edo \351:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign( 'q');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "edo:=diff(q(x),x,x ,x)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$edoG/-%%diffG6$-%\"qG6#% \"xG-%\"$G6$F,\"\"$\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "eq1:=q(63)=sin(63);\neq2:=q(-63)=sin(-63);\neq3:=D(q)(-63)=D(sin)(-63 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/-%\"qG6#\"#j-%$sinGF(" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/-%\"qG6#!#j,$-%$sinG6#\"#j!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/--%\"DG6#%\"qG6#!#j-%$co sG6#\"#j" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "dsolve(\{edo,eq 1,eq2,eq3\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"qG6#%\"xG,**&#\" \"\"\"\"#F+*&,&*&#F+\"%pRF+-%$sinG6#\"#jF+F+*&#F+F5F+-%$cosGF4F+!\"\"F +)F'F,F+F+F+*&#F+F5F+*&F2F+F'F+F+F+*&#F+F,F+F2F+F:*&#F5F,F+F8F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "q:=unapply(rhs(%),x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,**&#\"\"\"\"\"#F/*&,&*&#F/\"%pRF/-%$sinG6#\"#jF/F/*&#F/F9F/-%$cosG F8F/!\"\"F/)9$F0F/F/F/*&#F/F9F/*&F6F/F@F/F/F/*&#F/F0F/F6F/F>*&#F9F0F/F " 0 "" {MPLTEXT 1 0 10 "q(A)=sinA;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%'RTABLEG6%\")c*QH(-%'MATRIXG6#7%7 %,$*&#\"\"#\"\"$\"\"\"-%$sinG6#\"#jF2!\"\",$*&#\"\"&\"\"(F2F3F2F2,$*& \"%NGF2-%$cosGF5F2F27%,$*&#F<\"\"*F2F3F2F2,$*&#F0F1F2F3F2F2,$*&\"%B8F2 F@F2F77%\"\"!FN,$F3F7%'MatrixG-F%6%\")?id$)F(FP" }}}{EXCHG {PARA 257 " " 0 "" {TEXT -1 18 "Um breve ap\352ndice:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 80 "Esbo\347o de uma Justificativa p ara o c\341lculo funcional no caso n\343o diagonaliz\341vel." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "J\341 vimos que em geral, se " }{XPPEDIT 18 0 "A=S*B*S^(-1)" "6#/%\"AG*(%\"SG\"\"\"% \"BGF')F&,$F'!\"\"F'" }{TEXT -1 36 ", e f \351 uma fun\347\343o anal \355tica, ent\343o " }{XPPEDIT 18 0 "f(A)=S*f(B)*S^(-1)" "6#/-%\"fG6#% \"AG*(%\"SG\"\"\"-F%6#%\"BGF*)F),$F*!\"\"F*" }{TEXT -1 59 ". Isso era \+ usado para o caso em que A era diagonaliz\341vel e " }{XPPEDIT 18 0 " \+ B=Lambda" "6#/%\"BG%'LambdaG" }{TEXT -1 65 " sua forma diagonal. Nesse caso, se q fosse um polin\364mio tal que " }{XPPEDIT 18 0 "q(lambda) \+ = f(lambda);" "6#/-%\"qG6#%'lambdaG-%\"fG6#F'" }{TEXT -1 21 " para tod o autovalor " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 25 " de \+ A, era f\341cil ver que " }{XPPEDIT 18 0 "f(A)=q(A)" "6#/-%\"fG6#%\"AG -%\"qG6#F'" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 92 "O Teorema \+ da Forma Can\364nica de Jordan nos diz que uma matriz A pode sempre se r escrita como " }{XPPEDIT 18 0 "A = S*J*S^(-1);" "6#/%\"AG*(%\"SG\"\" \"%\"JGF')F&,$F'!\"\"F'" }{TEXT -1 7 ", onde " }{XPPEDIT 18 0 "J" "6#% \"JG" }{TEXT -1 50 " tem uma forma razoavelmente simples. No caso 2x2 \+ " }{XPPEDIT 18 0 "J" "6#%\"JG" }{TEXT -1 23 " \351 da forma diagonal o u" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "J:=JordanBlockMatrix([[lambda,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'RTABLEG6%\")w,A%)-%'MATRIXG6#7$7$%'lambdaG \"\"\"7$\"\"!F.%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Ora, \+ calcular " }{XPPEDIT 18 0 "f(J)" "6#-%\"fG6#%\"JG" }{TEXT -1 64 " \351 uma tarefa que podemos fazer na m\343o, dada a forma simples de " } {XPPEDIT 18 0 " J" "6#%\"JG" }{TEXT -1 0 "" }{TEXT -1 47 ". Se a fun \347\343o \351 uma s\351rie de pot\352ncia, digamos " }{XPPEDIT 18 0 " f(x)=sum(c[i]*x^i,i=0..infinity)" "6#/-%\"fG6#%\"xG-%$sumG6$*&&%\"cG6# %\"iG\"\"\")F'F/F0/F/;\"\"!%)infinityG" }{TEXT -1 75 ", podemos mandar o Maple fazer as contas, ao menos para uma subsoma finita:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('c');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "c[0]*IdentityMatrix(2)+sum(c[i]*J^i ,i=1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\");/z')-%'MA TRIXG6#7$7$,.&%\"cG6#\"\"!\"\"\"*&&F.6#F1F1%'lambdaGF1F1*&&F.6#\"\"#F1 )F5F9F1F1*&&F.6#\"\"$F1)F5F>F1F1*&&F.6#\"\"%F1)F5FCF1F1*&&F.6#\"\"&F1) F5FHF1F1,,F3F1*(F9F1F7F1F5F1F1*(F>F1F " 0 "" {MPLTEXT 1 0 35 "J:=J ordanBlockMatrix([[lambda,3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"JG-%'RTABLEG6%\")_=6&)-%'MATRIXG6#7%7%%'lambdaG\"\"\"\"\"!7%F0F.F/7% F0F0F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "c[0]*Ide ntityMatrix(3)+sum(c[i]*J^i,i=1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'RTABLEG6%\")sYi))-%'MATRIXG6#7%7%,.&%\"cG6#\"\"!\"\"\"*&&F.6#F1F1 %'lambdaGF1F1*&&F.6#\"\"#F1)F5F9F1F1*&&F.6#\"\"$F1)F5F>F1F1*&&F.6#\"\" %F1)F5FCF1F1*&&F.6#\"\"&F1)F5FHF1F1,,F3F1*(F9F1F7F1F5F1F1*(F>F1FF1F " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "70 0 0" 21 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 72126168 73048188 85786780 88093460 88106604 88155064 88173168 84645176 86439184 84071240 85909768 84645272 87000588 88050080 84633000 84727936 84914112 83576220 87137880 72938956 84220176 86790416 85111852 88624672 }{RTABLE M7R0 I5RTABLE_SAVE/72126168X,%)anythingG6"6"[gl!"%!!!#1"%"%!#**!#x"#)*"#B!#S"#j"#Z!# &)!#)*!#\"#&*""%"#g!#P"#PF'F& } {RTABLE M7R0 I5RTABLE_SAVE/73048188X*%)anythingG6"6"[gl!#%!!!"%"%^$$"+lz)Q0"!"($!*z*4+K!#=^$ $"*nU@W$!")$"+IV4<6!#<^$$!+Hmy0UF1$!+'3@aM"F4^$$!+H2tn5F*$"+NvF.EF-F& } {RTABLE M7R0 I5RTABLE_SAVE/85786780X,%)anythingG6"6"[gl!"%!!!#1"%"%^$$"+ztS>p!#5$!+kQgeX!#?^ $$!+Q$=R@#!"*$"+z*\^$$"+&[XtF(!#6$"+bt=CEF-$"""""!^$$!+RP?p=!")$"+]_C(G"! #;^$$!+/&yX@&F1$"+&H#*QM&!#<^$$"+5a*zA#FA$!+JYSU:FDF;^$$!+l!onz(F1$"+[[mz@FJ^$$ !+q!)z*[#F1$"+:3DL6FJ^$$"+L,uehF1$!+O(og$=FJF;^$$!+v!ok\"F1$!+G&zC1)F4^$$!+B'Gy %GF*$!+&>D#=zF-^$$"+tL(y4'F*$"+iLKA")!#@F;F& } {RTABLE M7R0 I5RTABLE_SAVE/88093460X,%)anythingG6#%)diagonalG6"[gl!"#!!!#%"%"%$"+lz)Q0"!"($" *nU@W$!")$!+Hmy0UF-$!+H2tn5F*F' } {RTABLE M7R0 I5RTABLE_SAVE/88106604X,%)anythingG6"6"[gl!"%!!!#1"%"%$"+ztS>p!#5$!+Q$=R@#!"*$" +&[XtF(!#6$"""""!$!+RP?p=!")$!+/&yX@&F,$"+5a*zA#F5F0$!+l!onz(F,$!+q!)z*[#F,$"+L ,uehF,F0$!+v!ok\"F,$!+B'Gy%GF)$"+tL(y4'F)F0F& } {RTABLE M7R0 I5RTABLE_SAVE/88155064X,%)anythingG6"6"[gl'"%!!!#1"%"%40523B0F2FAB59DAC06D2A4F6 456BACF401EAD93AC32B806405A58E1ED7189BBC05015CD5FB9F9EDC031F3067ACC01CC40532C35 D4C58C13400B897B121A095440747EA5980A9219405A2DCC537E09FAC07030601EF58E8DC045076 8407724B74063F90A32A9FB85403E683A73F989DDC05046F7B4FD0A47C05AB17A0783539DF& } {RTABLE M7R0 I5RTABLE_SAVE/88173168X,%)anythingG6"6"[gl'"%!!!#1"%"%40523B0F2E83005BC06D2A4F5 FB4DCCE401EAD9332627BB8405A58E20AB71327C05015CD5D75765BC031F306D7F4995E40532C35 C0398E49400B8982189E876A40747EA598A3D2E0405A2DCC4C1B59FAC0703060210F62E4C045076 8299F8BA14063F90A32AB89C6403E683A69D17CF0C05046F7B0BA9478C05AB17A06C1BB21F& } {RTABLE M7R0 I5RTABLE_SAVE/84645176X,%)anythingG6"6"[gl!"%!!!#1"%"%""!F'F'F'F'F'F'F'F'F'F'F' F'F'F'F'F& } {RTABLE M7R0 I5RTABLE_SAVE/86439184X,%)anythingG6"6"[gl'"%!!!#1"%"%400902B5E84001083FF62D5AF BD7AFDDC0065DA411CB3729BFE144B0B1B5B08140076056B441BB8C3FB93150BBF76AF0C0023237 CCB9C64F3FA5EED29E587D3D400B3AD035038F4E3FF31AC294288549C00854CF966F8766BFDBC6F 735C416A2400AFD1E4A2093263FF5CC8BE014F57DC0079D48DDAE354CBFDF55F82C4007AAF& } {RTABLE M7R0 I5RTABLE_SAVE/84071240X,%)anythingG6"6"[gl!"%!!!#1"%"%$"+>@`q6!"$$"+*yp$yS!")$! +^]YRu!"&$!+`_E<7F)$"+V)z16"F/$"+;Y$[="F,$"+F,F0FF,F0FF,F0F8"#5FAF'F& }