{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 "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 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 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 "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 32 "TD 7 : Alg\350bre lin\351 aire g\351n\351rale" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "restart:with(linalg):with(plots):alias(Id =&*()):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names n orm and trace have been redefined and unprotected\n" }}{PARA 7 "" 1 " " {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} }{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Le package Linalg" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "A:=matrix(3, 3, [1, 0, 0, 0, -2, - 9, 0, 1, 4]):\n'(A-Id)^2'=evalm((A-Id)^2):\n'A^n'=evalm(Id+n*(A-Id)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%\"AG%\"nG-%'matrixG6#7%7%\"\"\" \"\"!F-7%F-,&F&!\"$F,F,,$F&!\"*7%F-F&,&F&\"\"$F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "f:=(i, j) -> if i>j then 0 else j-i+1 fi:\n A:=matrix(5, 5, f):\n'A^(-1)'=evalm(A^(-1));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&\"\"\"F%%\"AG!\"\"-%'matrixG6#7'7'F%!\"#F%\"\"!F.7'F .F%F-F%F.7'F.F.F%F-F%7'F.F.F.F%F-7'F.F.F.F.F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "v:=[a, b, c, d]: M:=vandermonde(v):\nfor i from 1 to 4 do\n M[i, 4]:=M[i, 4]*v[i]:\nod:\nM=evalm(M);\n'det(M)'=facto r(det(M));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"MG-%'matrixG6#7&7&\" \"\"%\"aG*$)F+\"\"#F**$)F+\"\"%F*7&F*%\"bG*$)F3F.F**$)F3F1F*7&F*%\"cG* $)F9F.F**$)F9F1F*7&F*%\"dG*$)F?F.F**$)F?F1F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$detG6#%\"MG,$*0,&%\"dG!\"\"%\"cG\"\"\"F.,&%\"aGF.F+ F,F.,&F0F.F-F,F.,&%\"bGF.F+F,F.,&F3F.F-F,F.,&F3F.F0F,F.,*F3F.F-F.F+F.F 0F.F.F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "A:=randmatrix(5, 5);\n'theoreme'=iszero(transpose(evalm(adjoint(A))&*A-det(A)*Id));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'!#&)!#b!#P!#N\" #(*7'\"#]\"#z\"#c\"#\\\"#j7'\"#d!#f\"#X!\")!#$*7'\"##*\"#V!#i\"#x\"#m7 '\"#a!\"&\"#**!#h!#]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)theoremeG%% trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "f:=(i, j) -> if i= j then 1+v[i]^2 else v[i]*v[j] fi:\nA:=matrix(3, 3, f);\nVp:=eigenvect s(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%,&\"\" \"F+*$)%\"aG\"\"#F+F+*&F.F+%\"bGF+*&F.F+%\"cGF+7%F0,&F+F+*$)F1F/F+F+*& F3F+F1F+7%F2F8,&F+F+*$)F3F/F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# VpG6$7%\"\"\"\"\"#<$-%'vectorG6#7%,$*&%\"cGF'%\"aG!\"\"F2\"\"!F'-F+6#7 %,$*&%\"bGF'F1F2F2F'F37%,**$)F0F(F'F'*$)F9F(F'F'F'F'*$)F1F(F'F'F'<#-F+ 6#7%*&F1F'F9F2F'*&F0F'F9F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 296 "A:=matrix(3, 3, [1, alpha, a, 1, beta, b, 1, delta, c]):\nP:=matr ix(3, 3, [1, 1, 1, 1, 0, -1, 1, -1, 0]):\nDi:=evalm(P^(-1)&*A&*P): eqn s:=Di[1, 2]=0:\nfor i from 1 to 3 do\n for j from 1 to 3 do\n if i <>j then eqns:=eqns, Di[i, j]=0: fi:\n od:\nod:\nsolve(\{eqns\});\nVp :=eigenvects(subs(%, evalm(A)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<( /%\"bG\"\"\"/%&alphaGF&/%\"cGF&/%&deltaGF&/%%betaGF&/%\"aGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VpG6$7%\"\"$\"\"\"<#-%'vectorG6#7%F(F(F(7 %\"\"!\"\"#<$-F+6#7%!\"\"F/F(-F+6#7%F5F(F/" }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 41 "Interpolation au sens des moindres carr\351s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "x:=[1.1, 1.9, 3.2, 4.0, 5.3]:\ny:= [1.6, 2.9, 4.9, 6.1, 8.1]:\nA:=matrix(5, 2, (i, j)-> if j=1 then x[i] \+ else 1 fi):\nsol:=linsolve(evalm(transpose(A)&*A), evalm(transpose(A)& *y)):\nalpha:=sol[1]; beta:=sol[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%&alphaG$\"+RBMU:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG$!+ \"*\\7Eh!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "p1:=plot([s eq([x[i], y[i]],i=1..5)], 0..6, 0..10, style=point, color=black, symbo l=box):\np2:=plot(x->alpha*x+beta, 0..6, 0..10):\ndisplay[plot](p1, p2 );" }}{PARA 13 "" 1 "" {GLPLOT2D 786 268 268 {PLOTDATA 2 "6&-%'CURVESG 6&7'7$$\"33+++++++6!#<$\"33+++++++;F*7$$\"3!***************=F*$\"3!*** ************GF*7$$\"3;+++++++KF*$\"3M+++++++\\F*7$$\"\"%\"\"!$\"3k**** *********4'F*7$$\"3#)*************H&F*$\"3k*************4)F*-%'COLOURG 6&%$RGBGF:F:F:-%'SYMBOLG6#%$BOXG-%&STYLEG6#%&POINTG-F$6$7S7$$F:F:$!3F+ ++\"*\\7Eh!#>7$$\"3%*******\\#HyI\"!#=$\"3P:wNDz]/9FY7$$\"33++]([kdW#F Y$\"3K')Q>@OffJFY7$$\"3++++v;\\DPFY$\"3*o_W[/rL8&FY7$$\"3W+++DB?rFY7$$\"3o****\\P\"*y&H'FY$\"3qTD3X'\\w4*FY7$$\"3e****\\(G[ W[(FY$\"3CHn(y*o4$4\"F*7$$\"3i****\\()fB:()FY$\"3Os(ze\\EHG\"F*7$$\"39 ++](Q=\"))**FY$\"3!ec)oP&[#z9F*7$$\"3(****\\P'=pD6F*$\"3;W%>A(4%\\n\"F *7$$\"33+++lN?c7F*$\"3eQAz%pMi(=F*7$$\"3-++]U$e6P\"F*$\"3U83?:V``?F*7$ $\"36+++&>q0]\"F*$\"3=')*zWpJJD#F*7$$\"3'******\\U80j\"F*$\"3;,axR'[NX #F*7$$\"35+++0ytb@F*$\"3s/Ex%o-t?$F* 7$$\"3'****\\(3wY_AF*$\"3w67H5\\\"GT$F*7$$\"3#)******HOTqBF*$\"3E!o\"e _!GZf$F*7$$\"37++v3\">)*\\#F*$\"3eqjN,cJ%z$F*7$$\"3:++DEP/BEF*$\"3M,P8 Y,P%)RF*7$$\"3=++](o:;v#F*$\"3]UydD@n#=%F*7$$\"3=++v$)[opGF*$\"3qhXF*7$$\"3&****\\(QIKHJF*$\"3% =Ei^;E_w%F*7$$\"3#****\\7:xWC$F*$\"30\")4QGK$G%\\F*7$$\"37++]Zn%)oLF*$ \"3Q#phBs`Y8&F*7$$\"3y******4FL(\\$F*$\"3$yg#HiI#GL&F*7$$\"3#)****\\d6 .BOF*$\"3FE%=)*4$pEbF*7$$\"3(****\\(o3lWPF*$\"3KcitHBF9dF*7$$\"3!***** \\A))ozQF*$\"3n0o<$3ZD#fF*7$$\"3e******Hk-,SF*$\"3')=q`77p4hF*7$$\"36+ ++D-eITF*$\"3*fkVd^2&4jF*7$$\"3u***\\(=_(zC%F*$\"3W54*\\yq0\\'F*7$$\"3 M+++b*=jP%F*$\"3WNZNj2_)o'F*7$$\"3g***\\(3/3(\\%F*$\"3c\\DRmixuoF*7$$ \"33++vB4JBYF*$\"3QD3:MpYpqF*7$$\"3u*****\\KCnu%F*$\"3'[p)4[E\")fsF*7$ $\"3s***\\(=n#f([F*$\"3Kp%z-(p3fuF*7$$\"3P+++!)RO+]F*$\"3s\\X&o#=,^wF* 7$$\"30++]_!>w7&F*$\"3?8Q-8FGZyF*7$$\"3O++v)Q?QD&F*$\"3_k0;x$G>/)F*7$$ \"3G+++5jyp`F*$\"3RybQFvy?#)F*7$$\"3<++]Ujp-bF*$\"3[&>)y(H!yD%)F*7$$\" 3++++gEd@cF*$\"3v^GPv#G\"4')F*7$$\"39++v3'>$[dF*$\"3+R!p2Y:Y!))F*7$$\" 37++D6EjpeF*$\"3+.gzS;s\"**)F*7$$\"\"'F:$\"3+****3%y#z#>*F*-FC6&FE$\"# 5!\"\"FRFR-%+AXESLABELSG6$Q!6\"Fi]l-%%VIEWG6$;FRF]]l;FR$Fd]lF:" 1 2 0 1 10 0 2 9 1 4 2 1.000000 43.000000 51.000000 0 0 "Curve 1" "Curve 2" }}}}}}{MARK "0 0 0" 4 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }