{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 "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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "#Exercice 1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7ir%#&xG%$AddG%(AdjointG%3BackwardSubs tituteG%+BandMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalFormG%-Bilinear FormG%%CAREG%5CharacteristicMatrixG%9CharacteristicPolynomialG%'Column G%0ColumnDimensionG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatrixG% 0ConditionNumberG%/ConstantMatrixG%/ConstantVectorG%%CopyG%2CreatePerm utationG%-CrossProductG%%DAREG%-DeleteColumnG%*DeleteRowG%,Determinant G%)DiagonalG%/DiagonalMatrixG%*DimensionG%+DimensionsG%+DotProductG%6E igenConditionNumbersG%,EigenvaluesG%-EigenvectorsG%&EqualG%2ForwardSub stituteG%.FrobeniusFormG%4GaussianEliminationG%2GenerateEquationsG%/Ge nerateMatrixG%(GenericG%2GetResultDataTypeG%/GetResultShapeG%5GivensRo tationMatrixG%,GramSchmidtG%-HankelMatrixG%,HermiteFormG%3HermitianTra nsposeG%/HessenbergFormG%.HilbertMatrixG%2HouseholderMatrixG%/Identity MatrixG%2IntersectionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*I sUnitaryG%2JordanBlockMatrixG%+JordanFormG%1KroneckerProductG%(LA_Main G%0LUDecompositionG%-LeastSquaresG%,LinearSolveG%.LyapunovSolveG%$MapG %%Map2G%*MatrixAddG%2MatrixExponentialG%/MatrixFunctionG%.MatrixInvers eG%5MatrixMatrixMultiplyG%+MatrixNormG%,MatrixPowerG%5MatrixScalarMult iplyG%5MatrixVectorMultiplyG%2MinimalPolynomialG%&MinorG%(ModularG%)Mu ltiplyG%,NoUserValueG%%NormG%*NormalizeG%*NullSpaceG%3OuterProductMatr ixG%*PermanentG%&PivotG%*PopovFormG%0QRDecompositionG%-RandomMatrixG%- RandomVectorG%%RankG%6RationalCanonicalFormG%6ReducedRowEchelonFormG%$ RowG%-RowDimensionG%-RowOperationG%)RowSpaceG%-ScalarMatrixG%/ScalarMu ltiplyG%-ScalarVectorG%*SchurFormG%/SingularValuesG%*SmithFormG%8Stron glyConnectedBlocksG%*SubMatrixG%*SubVectorG%)SumBasisG%0SylvesterMatri xG%/SylvesterSolveG%/ToeplitzMatrixG%&TraceG%*TransposeG%0TridiagonalF ormG%+UnitVectorG%2VandermondeMatrixG%*VectorAddG%,VectorAngleG%5Vecto rMatrixMultiplyG%+VectorNormG%5VectorScalarMultiplyG%+ZeroMatrixG%+Zer oVectorG%$ZipG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "? 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"" 1 " " {XPPMATH 20 "6'7#-%'RTABLEG6%\"*[,8i\"-%'MATRIXG6#7$7#\"\"\"7#\"\"%& %'VectorG6#%'columnG7'-F%6%\"*;48i\"-F)6#7'F,7#\"\"!F;F;F;F0-F%6%\"*!) 48i\"-F)6#7'F;F,F;F;F;F0-F%6%\"*W58i\"-F)6#7'F;F;F,F;F;F0-F%6%\"*368i \"-F)6#7'F;F;F;F,F;F0-F%6%\"*s68i\"-F)6#7'F;F;F;F;F,F07'-F%6%\"*/C^j\" -F)6#7)F,F;F;F;F;7##!)&\\i+&\")'z'eV7##\")\\QfmFinF0-F%6%\"*oC^j\"-F)6 #7)F;F,F;F;F;7##\"*2pJ=#\"*cQR!Q7##!(4c^*FfoF0-F%6%\"*KD^j\"-F)6#7)F;F ;F,F;F;7##!*&3x(z#\"*_:/B&7##\"*fLM(\\FcpF0-F%6%\"*'f7N;-F)6#7)F;F;F;F ,F;7##!+h!=**)H\"+;CL%=%7##\"+ry2@\\F`qF0-F%6%\"*gE^j\"-F)6#7)F;F;F;F; F,7##\")N-+A\")Gd6e7##!)XnRCF]rF07'-F%6%\"*GM^j\"FYF0-F%6%\"*#\\8N;F`o F0-F%6%\"*cN^j\"F]pF0-F%6%\"*?O^j\"FjpF0-F%6%\"*%o8N;FgqF07$-F%6%\"*_W ^j\"-F)6#7$F,F;F0-F%6%\"*;X^j\"-F)6#7$F;F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "#Les matrices R2 et R ont la m\352me image." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "seq3:=A,B,R,H;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%seq3G6&-%'RTABLEG6%\"*?\"f5;-%'MATRIXG6#7$7$ 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"6#>%\"XG-%'RTABLEG6%\"*wWMy\"-%'MATRIXG6#7$7$^#\"\"\"^#!\"\"7$F/F/ %'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "X.Matrix([[Eig envectors(B)[1][1],0],[0,Eigenvectors(B)[1][2]]]).X^(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*%[s(z\"-%'MATRIXG6#7$7$\"\"\"!\" &7$\"\"&F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval f(Eigenvalues(R));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*w -_#=-%'MATRIXG6#7)7#$\"\"!F-F+7#$\"0gg-m9*y?!#67#$\"0ufC['\\qxF17#$\"0 x8t%3U)o\"!#57#$!0UfE`z1.\"F87#$!0QE*GCG%H\"F8&%'VectorG6#%'columnG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalf(Eigenvalues(H));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*sTD'=-%'MATRIXG6#7,7#$ \"0L1+(4_n?!#G7#$\"0MJQs>Kb%!#E7#$\"0O\\W@a8h%!#C7#$\"0$p)[4&\\WG!#A7# $\"07&HjYk#>\"!#?7#$\"0XlDib**e$!#>7#$\"07:0)4P!)z!#=7#$\"0cMB;!*[K\"! #;7#$\"0g-5^tti\"!#:7#$\"0dlgriwG\"!#9&%'VectorG6#%'columnG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 305 "#H est diagonalisable. Pour r\351pondre \340 la question pr\351c\351dente \340 savoir si J est di agonalisable il faut calculer la dimension de l'espace propre associ \351 \340 la valeur 0, c'est \340 dire le noyau. Or nous avions calcul \351 une base du noyau qui \351tait compos\351 de deux vecteurs. Cette matrice est donc diagonalisable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }