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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 
257 27 "G\351om\351trie affine analytique" }{TEXT 260 1 "\n" }{TEXT 
258 19 "Exercice 11 du poly" }{TEXT 259 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 103 "f1:=vector([-1,1,1]):f2:=vector([1,-1,1]):f3:=vec
tor([1,1,-1]):M0:=vector([3,-1,0]):M:=vector([x,y,z]):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "det(matrix([f1,f2,f3]));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "On a donc
 une base, et les espaces F et G sont bien suppl\351mentaires" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "l:=solve(det(matrix([evalm(M
-M0-lambda*f3),f1,f2]))=0,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"lG,(%\"xG#\"\"\"\"\"#F(!\"\"*&F'F(%\"yGF(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "p_de_m:=evalm(M-l*f3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'p_de_mG-%'vectorG6#7%,(%\"xG#\"\"\"\"\"#F,F,*&#F,F-F
,%\"yGF,!\"\",(F0F+*&#F,F-F,F*F,F1F,F,,*%\"zGF,*&F+F,F*F,F,F,F1*&F+F,F
0F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "genmatrix(convert(
p_de_m,list),[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#
7%7%#\"\"\"\"\"##!\"\"F*\"\"!7%F+F(F-7%F(F(F)" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 81 "C'est la matrice de la partie lin\351aire dans la base
 canonique. Que v\351rifie-t-on ?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "sym_de_m:=evalm(p_de_m-(M-p_de_m));" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%)sym_de_mG-%'vectorG6#7%,&\"\"#\"\"\"%\"yG!\"\",&%
\"xGF-F*F+,*%\"zGF+F/F+F*F-F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 42 "genmatrix(convert(sym_de_m,list),[x,y,z]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"!!\"\"F(7%F)F(F(7%\"\"\"F,F," }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "V\351rifications ?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "aff_de_m:=evalm(p_de_m-2*(M-p_de_m)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)aff_de_mG-%'vectorG6#7%,(%\"x
G#!\"\"\"\"#\"\"$\"\"\"*&#F.F-F/%\"yGF/F,,(F2F+*&#F.F-F/F*F/F,F.F/,*%
\"zGF/*&#F.F-F/F*F/F/F.F,*&F9F/F2F/F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "genmatrix(convert(aff_de_m,list),[x,y,z]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%#!\"\"\"\"##!\"$F*\"\"!7%F+F
(F-7%#\"\"$F*F0\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "V\351rif
ications ?" }}}}{MARK "3 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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