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0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 340 1 {CSTYLE "" -1 
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 13 "Calcul Formel" }{TEXT 
-1 18 " MASS 1 2003-2004\n" }{TEXT 257 9 "Feuille 8" }{TEXT -1 36 "   \+
Alg\350bre lin\351aire  et Statistiques" }}{PARA 256 "" 0 "" {TEXT -1 
54 "                   Analyse en composantes principales." }}}{EXCHG 
{PARA 340 "> " 0 "" {MPLTEXT 1 0 26 "with(linalg): with(plots):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{SECT 0 {PARA 341 "" 0 "" {TEXT -1 18 "Un premier exemple" }}{PARA 
261 "" 0 "" {TEXT 294 63 "Dans cette partie, on s'int\351resse au tabl
eau de notes suivant :" }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 167 
"nb_notes := 100:\nNotes:=matrix(nb_notes,2):\nfor i from 1 to nb_note
s do\n   Notes[i,1]:=rand(1..20)();\n   Notes[i,2]:= max( min( Notes[i
,1]+ rand(-3..3)(),20 ), 0);\nod:" }}}{PARA 268 "" 0 "" {TEXT -1 260 "
 A chaque \351tudiant  est attribu\351 un num\351ro (de 1 \340 nb_note
s).\nLa k-i\350me ligne de ce tableau correspond aux notes de l'\351tu
diant n\260 k. La premi\350re colonne correspond aux notes obtenues \+
\340 l'examen et la seconde aux notes obtenues au partiel de milieu de
 semestre." }}{SECT 0 {PARA 266 "" 0 "" {TEXT -1 31 "Affichage de \"nu
ages de points\"" }{TEXT 258 132 "\nPour visualiser ce tableau de donn
\351es, on peut afficher  les points dont les  coordonn\351es sont : n
ote de l'examen, note du partiel." }}{EXCHG {PARA 269 "> " 0 "" 
{MPLTEXT 1 0 57 "ens_points:=\{seq([Notes[i,1],Notes[i,2]],i=1..nb_not
es)\}:" }}}{EXCHG {PARA 270 "> " 0 "" {MPLTEXT 1 0 22 "pointplot(ens_p
oints);" }}{PARA 271 "" 1 "" {GLPLOT2D 502 140 140 {PLOTDATA 2 "6#-%'P
OINTSG6fo7$$\"#7\"\"!$\"#5F)7$$\"#?F)$\"#>F)7$$\"\"'F)$\"\"%F)7$F*$\"
\"*F)7$$\"#<F)$\"#=F)7$$\"\")F)F?7$$\"\"\"F)F)7$F7F77$FBF47$F7F'7$F7F*
7$F-F<7$$\"#8F)$\"#9F)7$$\"#;F)FL7$FLFL7$FL$\"#6F)7$F?F77$F7F?7$F?F27$
F4FB7$F*F'7$F'FS7$F/F/7$FL$\"#:F)7$F*FS7$FJFgn7$F'FL7$F<FO7$F/F-7$$\"
\"$F)F27$$\"\"(F)F77$F?Fbo7$FOFO7$$\"\"#F)FB7$FLF'7$F<F/7$FBFB7$F2F77$
F7Fbo7$F_oF47$F<F<7$F_oF)7$F/F:7$F<Fgn7$FSF?7$F*F*7$FOFJ7$FJF'7$F4F_o7
$F?F*7$F4$\"\"&F)7$FboFbo7$FOF/7$FgnF:7$F2F_o7$F-F-7$FLF:7$F_oFB7$FSF7
7$F*FJ7$FSFJ7$F:F-7$F_oFjp7$F4Fbo7$F<F-7$FOF<7$FjpF_o7$FboF*7$FjpF27$F
jpFjp7$FJFS7$FSF*7$F2Fjp7$F/FO" 1 2 0 1 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 }}}}}{SECT 0 {PARA 267 "" 0 "" {TEXT -1 19 "Moye
nne, Ecart-type" }}{EXCHG {PARA 272 "" 0 "" {TEXT -1 42 "Soit L une \"
liste\" de donn\351es num\351riques :" }}}{EXCHG {PARA 273 "> " 0 "" 
{MPLTEXT 1 0 32 "L:=[seq(rand(1..20)(),k=1..20)]:" }}}{PARA 275 "" 0 "
" {TEXT -1 90 "On peut en calculer la moyenne de la fa\347on suivante \+
(on utilise la fonction add de Maple )" }}{EXCHG {PARA 276 "> " 0 "" 
{MPLTEXT 1 0 32 "somme := add(L[i],i=1..nops(L)):" }}}{EXCHG {PARA 
277 "> " 0 "" {MPLTEXT 1 0 32 "moyenne:=evalf(somme/nops(L)): \n" }
{TEXT -1 40 "#  nops(L) est le nombre d'\351l\351ments de L" }}}{PARA 
279 "" 0 "" {TEXT -1 45 "Et l'\351cart-type en utilisant la d\351finit
ion : " }}{EXCHG {PARA 280 "> " 0 "" {MPLTEXT 1 0 60 "somme_carres_des
_ecarts:=add((L[i]-moyenne)^2,i=1..nops(L)):" }}}{EXCHG {PARA 281 "> \+
" 0 "" {MPLTEXT 1 0 57 "ecart_type:=evalf(sqrt(somme_carres_des_ecarts
/nops(L))):" }}}{EXCHG {PARA 283 "" 0 "" {TEXT -1 34 "ou bien , apr
\350s un savant calcul :" }}}{EXCHG {PARA 284 "> " 0 "" {MPLTEXT 1 0 
97 "somme_carres:=add(L[i]^2,i=1..nops(L)):\necart_type:=evalf(sqrt( s
omme_carres/nops(L)-moyenne^2)):" }}}{EXCHG {PARA 286 "" 0 "" {TEXT 
-1 68 "Pour \351viter ces formules \"barbares\",  on peut \351crire de
ux fonctions:" }}}{EXCHG {PARA 287 "> " 0 "" {MPLTEXT 1 0 230 "moyenne
_stat:=proc(L)\nlocal s,i;\n  s:=add(L[i],i=1..nops(L)):\n  RETURN(eva
lf(s/nops(L)));\nend:\n\necart_type_stat:=proc(L)\nlocal s,i,m;\n  s:=
add(L[i]^2,i=1..nops(L)):\n  m:= moyenne_stat(L);\n  RETURN(evalf(sqrt
(s/nops(L)-m^2)));\nend:" }}}{PARA 288 "" 0 "" {TEXT -1 1 "\n" }{TEXT 
260 2 "Q1" }{TEXT -1 165 " (i) Calculer les  moyennes de la promotion \+
pour l'examen et  pour le partiel.\n      (ii) Calculer les \351carts-
type de la promotion pour l'examen et pour le partiel.\n" }}{SECT 1 
{PARA 289 "" 0 "" {TEXT 289 8 "R\351ponses" }}{EXCHG {PARA 290 "> " 0 
"" {MPLTEXT 1 0 159 "Examen:= [seq(Notes[i,1],i=1..nb_notes)]:\nPartie
l:=[seq(Notes[i,2],i=1..nb_notes)]:\nmoyenne_exam:=moyenne_stat(Examen
):\nmoyenne_partiel:=moyenne_stat(Partiel):" }}}{EXCHG {PARA 293 "> " 
0 "" {MPLTEXT 1 0 41 "ecart_type_exam:=ecart_type_stat(Examen):" }}}
{EXCHG {PARA 295 "> " 0 "" {MPLTEXT 1 0 45 "ecart_type_partiel:=ecart_
type_stat(Partiel):" }}}{EXCHG {PARA 297 "> " 0 "" {MPLTEXT 1 0 73 "va
riance_exam:=ecart_type_exam^2:\nvariance_partiel:=ecart_type_partiel^
2:" }}}}{PARA 300 "" 0 "" {TEXT -1 1 "\n" }{TEXT 261 2 "Q2" }{TEXT -1 
280 "  Calculer la matrice C obtenue \340 partir de la matrice Notes e
n retranchant \340 chaque note de la premi\350re colonne la moyenne de
 l'examen et \340 chaque note de la deuxi\350me colonne la moyenne du \+
partiel.\n     Pour cela , \351crire une boucle pour \"remplir\" la ma
trices C  d\351clar\351e  ainsi:" }}{EXCHG {PARA 301 "> " 0 "" 
{MPLTEXT 1 0 23 "C:= matrix(nb_notes,2):" }}}{SECT 1 {PARA 302 "" 0 "
" {TEXT 286 7 "R\351ponse" }}{EXCHG {PARA 303 "> " 0 "" {MPLTEXT 1 0 
102 "for i to nb_notes do\n   C[i,1]:= Notes[i,1]-moyenne_exam:\n   C[
i,2]:= Notes[i,2]-moyenne_partiel: \nod:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 288 11 "Pour voir :" }}}{EXCHG {PARA 304 "> " 0 "" {MPLTEXT 1 0 
9 "evalm(C):" }}}}}{SECT 0 {PARA 305 "" 0 "" {TEXT -1 58 "Diagonalisat
ion de la matrice des \"variances-covariances\"\n" }{TEXT 263 75 "On s
'int\351resse maintenant \340 la matrice suivante (dite matrice des va
riances" }{TEXT -1 1 "-" }{TEXT 284 14 "covariances) :" }}{EXCHG 
{PARA 306 "> " 0 "" {MPLTEXT 1 0 26 "M:=evalm(transpose(C)&*C):" }}}
{EXCHG {PARA 307 "" 0 "" {TEXT -1 8 "On note " }{TEXT 287 1 "a" }
{TEXT -1 70 " le coefficient de M le plus grand en valeur absolue et o
n change  M :" }}}{EXCHG {PARA 308 "> " 0 "" {MPLTEXT 1 0 19 "M:=evalm
(M/abs(a)):" }}}{PARA 309 "" 0 "" {TEXT 264 69 "Vous remarquerez que M
 est sym\351trique; on peut donc la diagonaliser.\n" }{TEXT 265 2 "Q3
" }{TEXT -1 102 " En utilisant la m\351thode de la feuille 5, d\351ter
miner les valeurs propres et les vecteurs propres de M." }}{SECT 1 
{PARA 310 "" 0 "" {TEXT 259 8 "R\351ponses" }}{EXCHG {PARA 311 "> " 0 
"" {MPLTEXT 1 0 26 "Id:=matrix(2,2,[1,0,0,1]):" }}}{EXCHG {PARA 312 ">
 " 0 "" {MPLTEXT 1 0 114 "M2:=Id:\nfor k from 1 to 200 do \n      M2:=
evalm(M2&*M): \nod:\nM3:=evalm(M2&*M):\ngrande_vp:=evalf(M3[1,1]/M2[1,
1]):\n" }}}{EXCHG {PARA 313 "> " 0 "" {MPLTEXT 1 0 123 "N:=inverse(M):
 N2:=Id:\nfor k from 1 to 200 do \n  N2:=evalm(N2&*N): od:\nN3:=evalm(
N2&*N):\npetite_vp:=evalf(N2[1,1]/N3[1,1]):" }}}{EXCHG {PARA 314 "> " 
0 "" {MPLTEXT 1 0 110 "K:=evalm((1/grande_vp)*M): \nS:=Id:\nfor k from
 1 to 200 do \n  S:=evalm(S&*K): \nod:\nv1:=vector([S[1,1],S[2,1]]);" 
}}{PARA 315 "" 1 "" {XPPMATH 20 "6#>%#v1G-%'vectorG6#7$$\"+Q\"yT([!#5$
\"+XmT)*\\F+" }}}{EXCHG {PARA 316 "> " 0 "" {MPLTEXT 1 0 106 "R:=evalm
(petite_vp*N): \nT:=Id:\nfor k from 1 to 200 do \n  T:=evalm(T&*R): \n
od:\nv2:=vector([T[1,1],T[2,1]]);" }}{PARA 317 "" 1 "" {XPPMATH 20 "6#
>%#v2G-%'vectorG6#7$$\"+4=#e7&!#5$!+6mT)*\\F+" }}{PARA 318 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 319 "" 1 "" {TEXT -1 0 "" }}}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 262 "" 0 "" {TEXT 262 17 "Affich
age complet" }{TEXT 270 211 "\nNotons :\n\227 m1 la moyenne de l'exame
n\n\227 m2 la moyenne du partiel\n\227 vp1 la plus grande valeur propr
e de M et v1 un vecteur propre associ\351\n\227 vp2 la plus petite val
eur propre de M et v2 un  vecteur propre associ\351 \n" }{TEXT 266 3 "
\nQ4" }{TEXT 268 1 " " }{TEXT 267 18 "Sur un m\352me dessin" }{TEXT 
269 9 ", tracer\n" }{TEXT 285 6 "      " }{TEXT 290 224 "\227 le nuage
 de points des notes de la promotion (celui de la partie \"Affichage\"
)\n      \227 la droite passant par le point (m1, m2) de vecteur direc
teur v1\n      \227 la droite passant par le point (m1, m2) de vecteur
 directeur v2\n" }{TEXT 298 31 "Consulter l'aide en ligne pour " }
{TEXT 295 5 "plot " }{TEXT 296 3 "et " }{TEXT 297 7 "display" }}{SECT 
1 {PARA 320 "" 0 "" {TEXT 291 8 "R\351ponses" }}{EXCHG {PARA 321 "> " 
0 "" {MPLTEXT 1 0 55 "norme:=proc(v)\nRETURN(sqrt(evalf(v[1]^2+v[2]^2)
));\nend:" }}}{EXCHG {PARA 322 "> " 0 "" {MPLTEXT 1 0 113 "m:=moyenne_
exam,moyenne_partiel: v1:=evalm(v1/norme(v1)): v2:=evalm(v2/norme(v2))
: q:=evalf(grande_vp/petite_vp):" }}}{EXCHG {PARA 323 "> " 0 "" 
{MPLTEXT 1 0 189 "graph1:=pointplot(\{seq([Notes[i,1],Notes[i,2]],i=1.
.nb_notes)\}):\ngraph2:=plot([m[1]+v1[1]*t,m[2]+v1[2]*t,t=-10..10],col
or=red):\ngraph3:=plot([m[1]+v2[1]*t,m[2]+v2[2]*t,t=-4..4],color=blue)
:" }}}{EXCHG {PARA 324 "> " 0 "" {MPLTEXT 1 0 32 "display(\{graph1,gra
ph2,graph3\});" }}{PARA 13 "" 1 "" {GLPLOT2D 296 293 293 {PLOTDATA 2 "
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^mA5Fiy7$$\"18Ypx_Z>6Fiy$\"1]T:ZZq55Fiy7$$\"1c-^DWZJ6Fiy$\"1=^O\\%Q+**
*Fjr7$$\"1wl+=U3V6Fiy$\"1Sw\"R?Eo()*Fjr7$$\"11$eJ\"\\(f:\"Fiy$\"1gw]2L
7^(*Fjr7$$\"1j*)3wxbn6Fiy$\"1<6AkO<Q'*Fjr7$$\"1I+ea\\#*z6Fiy$\"1'4%R6e
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(zyC))G*Fjr7$$\"1uFO')4\"\\@\"Fiy$\"1vNUp9Tw\"*Fjr7$$\"1&)>BD4'pA\"Fiy
$\"1A[6hr!*e!*Fjr7$$\"1P\\+V>uQ7Fiy$\"1#)3\">ADS%*)Fjr7$$\"1;`!odv5D\"
Fiy$\"1c$o#yWvB))Fjr7$$\"1IA/KV&HE\"Fiy$\"1]Oid%>zq)Fjr7$$\"13'e\\2-^F
\"Fiy$\"1-<f=9Y*e)Fjr7$$\"1v.VG#\\rG\"Fiy$\"186$>F%)>Z)Fjr7$$\"1r>I6$>
#)H\"Fiy$\"1,X&[(\\.k$)Fjr7$$\"1J5`vo!4J\"Fiy$\"1yFL)*GJS#)Fjr7$$\"1aq
A%yaAK\"Fiy$\"1n,>)Ra'H\")Fjr7$$\"1!Hb<-aVL\"Fiy$\"1&Q^nNp;,)Fjr7$$\"1
Lx*e`MfM\"Fiy$\"1-Ca<Eu)*yFjr7$$\"1++))z$z$e8Fiy$\"1+++9uQxxFjr-F_bl6&
FablF)F)Fbbl-%+AXESLABELSG6$%!GFbbm-%%VIEWG6$%(DEFAULTGFfbm" 1 2 0 1 
0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}}{SECT 0 {PARA 257 "" 0 "" {TEXT -1 14 "Cas d'un nuage" }
{TEXT 276 1 " " }{TEXT -1 34 "concentr\351 au voisinage d'une droit" }
{TEXT 274 1 "e" }{TEXT 275 1 "\n" }{TEXT 272 239 "Dans cette partie, o
n se place dans le cas d'un tableau de donn\351es dont le nuage de poi
nts est plus ou moins concentr\351 au voisinage d'une droite.\nOn peut
 obtenir un tel tableau de donn\351es en faisant, par exemple, la cons
truction suivante :" }}{EXCHG {PARA 325 "> " 0 "" {MPLTEXT 1 0 163 "Ta
b:=matrix(100,2): u:=rand(1..30)()/10: v:=rand(1..20)()/10:nb:=100:\nf
or i to nb do \n   Tab[i,1]:=i*0.1:\n   Tab[i,2]:= evalf(u*Tab[i,1]+v+
rand(-10..10)()/20) \nod:" }}}{EXCHG {PARA 326 "> " 0 "" {MPLTEXT 1 0 
46 "pointplot(\{seq([Tab[i,1],Tab[i,2]],i=1..nb)\});" }}{PARA 13 "" 1 
"" {GLPLOT2D 530 166 166 {PLOTDATA 2 "6#-%'POINTSG6`q7$$\"\"\"!\"\"$\"
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?AF,7$$\"\"&F)$\"++++]>F,7$$\"\"'F)$\"++++!G#F,7$$\"\"(F)$\"++++g?F,7$
$\"\")F)$\"++++!4$F,7$$\"\"*F)$\"++++qDF,7$$\"#5F)$\"++++]DF,7$$\"#6F)
$\"++++IHF,7$$\"##)F)$\"++++Y7!\")7$$\"#$)F)$\"++++47F^o7$$\"#%)F)$\"+
+++s7F^o7$$\"#&)F)$\"++++:7F^o7$$\"#')F)$\"++++$G\"F^o7$$\"#()F)$\"+++
+T8F^o7$$\"#))F)$\"++++p7F^o7$$\"#*)F)$\"++++n7F^o7$$\"#!*F)$\"+++++8F
^o7$$\"#\"*F)$\"++++)Q\"F^o7$$\"##*F)$\"++++18F^o7$$\"#$*F)$\"++++z8F^
o7$$\"#%*F)$\"++++29F^o7$$\"#&*F)$\"++++q8F^o7$$\"#'*F)$\"++++[9F^o7$$
\"#(*F)$\"++++E9F^o7$$\"#)*F)$\"++++u9F^o7$$\"#**F)$\"++++i9F^o7$$\"$+
\"F)$\"++++g9F^o7$$\"#ZF)$\"++++5#)F,7$$\"#[F)$\"++++SyF,7$$\"#\\F)$\"
++++q\")F,7$$\"#]F)$\"++++]\")F,7$$\"#^F)$\"++++!)zF,7$$\"#_F)$\"++++5
!)F,7$$\"#`F)$\"++++!z)F,7$$\"#aF)$\"++++q&)F,7$$\"#bF)$\"+++++!*F,7$$
\"#cF)$\"++++!o)F,7$$\"#dF)$\"++++g!*F,7$$\"#eF)$\"++++!R*F,7$$\"#fF)$
\"++++q*)F,7$$\"#gF)Fdw7$$\"#hF)$\"++++!3*F,7$$\"#iF)$\"++++g)*F,7$$\"
#jF)$\"++++S'*F,7$$\"#kF)$\"++++?'*F,7$$\"#lF)$\"++++05F^o7$$\"#mF)$\"
++++[5F^o7$$\"#nF)$\"++++c5F^o7$$\"#oF)$\"++++S**F,7$$\"#pF)$\"++++26F
^o7$$\"#qF)$\"++++g5F^o7$$\"#rF)$\"++++o5F^o7$$\"#sF)$\"++++Y5F^o7$$\"
#tF)$\"++++u5F^o7$$\"#uF)$\"++++_6F^o7$$\"#vF)$\"++++l6F^o7$$\"#wF)$\"
++++)=\"F^o7$$\"#xF)$\"++++,7F^o7$$\"#yF)$\"++++R6F^o7$$\"#zF)$\"++++(
>\"F^o7$$\"#!)F)$\"++++?7F^o7$$\"#\")F)$\"++++Q7F^o7$$\"#7F)$\"++++5JF
,7$$\"#8F)$\"++++SIF,7$$\"#9F)$\"++++qKF,7$$\"#:F)$\"++++]QF,7$$\"#;F)
$\"++++IKF,7$$\"#<F)$\"++++gQF,7$$\"#=F)$\"++++SQF,7$$\"#>F)$\"++++?UF
,7$$\"#?F)$\"++++]WF,7$$\"#@F)$\"++++![%F,7$$\"#AF)$\"++++gXF,7$$\"#BF
)$\"++++!z%F,7$$\"#CF)$\"++++q[F,7$$\"#DF)$\"+++++YF,7$$\"#EF)$\"++++!
Q&F,7$$\"#FF)$\"++++5ZF,7$$\"#GF)$\"++++S]F,7$$\"#HF)$\"++++?aF,7$$\"#
IF)$\"+++++dF,7$$\"#JF)F_dl7$$\"#KF)$\"++++5aF,7$$\"#LF)$\"++++SiF,7$$
\"#MF)$\"++++?lF,7$$\"#NF)$\"+++++kF,7$$\"#OF)$\"++++!Q'F,7$$\"#PF)$\"
++++gkF,7$$\"#QF)$\"++++ShF,7$$\"#RF)$\"++++?mF,7$$\"#SF)$\"+++++nF,7$
$\"#TF)$\"++++!e'F,7$$\"#UF)$\"++++5tF,7$$\"#VF)$\"++++!*pF,7$$\"#WF)$
\"++++?vF,7$$\"#XF)$\"++++]uF,7$$\"#YF)$\"++++!3)F," 1 2 0 1 0 2 9 1 
4 2 1.000000 45.000000 45.000000 0 }}}}{PARA 0 "" 0 "" {TEXT -1 1 "\n
" }{TEXT 271 140 "On  peut d\351terminer la droite \"la plus proche\" \+
du nuage en un sens qu'on vous a peut-etre pr\351cis\351 dans le Cours
 de Statistiques (mot-clef : " }{TEXT 292 20 "droite de r\351gression
" }{TEXT 293 96 ").\nSi elle a pour \351quation y = a x + b, le calcul
 des coefficients a et b est donn\351 ci-dessous :" }}{EXCHG {PARA 
327 "> " 0 "" {MPLTEXT 1 0 157 "mTab1:= add(Tab[i,1],i=1..nb)/nb:\nmTa
b2:= add(Tab[i,2],i=1..nb)/nb:\ncov1_2:= add(Tab[i,1]*Tab[i,2],i=1..nb
)/nb:\nvar1:= add(Tab[i,1]^2,i=1..nb)/nb - mTab1^2: " }}}{EXCHG {PARA 
328 "> " 0 "" {MPLTEXT 1 0 72 "a:=(cov1_2-mTab1*mTab2)/var1:\nb:=mTab2
 - mTab1*a:\nregression:= x->a*x+b:" }}}{EXCHG {PARA 329 "> " 0 "" 
{MPLTEXT 1 0 32 "plot([x,regression(x),x=0..10]):" }}}{PARA 330 "" 0 "
" {TEXT -1 1 "\n" }{TEXT 279 2 "Q5" }{TEXT 281 136 " (i) Calculer la m
atrice des variances-covariances associ\351e \340 Tab, d\351terminer s
a plus grande valeur propre et un vecteur propre associ\351." }}{PARA 
331 "" 0 "" {TEXT -1 87 "      (ii) Comment pourrait-on calcul plus di
rectement cette matrice (\"papier-crayon\"!)" }}{PARA 0 "" 0 "" {TEXT 
282 11 "      (ii) " }{TEXT 278 18 "Sur un m\352me dessin" }{TEXT 280 
280 ", tracer\n            \227 le nuage de points associ\351 \340 Tab
.\n            \227 la droite passant par le point m (de coordonn\351e
s les moyennes de chacune des colonnes de Tab) et de \"vecteur-directe
ur\" le vecteur  propre calcul\351 en (i). \n            \227 la droit
e de r\351gression associ\351e \340 Tab." }}{SECT 1 {PARA 332 "" 0 "" 
{TEXT -1 8 "R\351ponses" }}{EXCHG {PARA 333 "> " 0 "" {MPLTEXT 1 0 53 
"m:=add(Tab[i,1],i=1..nb)/nb,add(Tab[i,2],i=1..nb)/nb:" }}}{EXCHG 
{PARA 334 "> " 0 "" {MPLTEXT 1 0 143 "C_Tab:=matrix(100,2): \nfor i to
 100 do\n  C_Tab[i,1]:=(Tab[i,1]-m[1]):\n  C_Tab[i,2]:=(Tab[i,2]-m[2])
 \nod:\nM_Tab:=evalm(transpose(C_Tab)&*C_Tab):" }}}{EXCHG {PARA 335 ">
 " 0 "" {MPLTEXT 1 0 44 "E:=eigenvectors(M_Tab): # trichons un peu...
" }}}{EXCHG {PARA 336 "> " 0 "" {MPLTEXT 1 0 29 "vp:= E[?][1]: v:=op(E
[?][3]):" }}}{EXCHG {PARA 337 "" 0 "" {TEXT 283 9 "ATTENTION" }{TEXT 
-1 68 "   ? = 1 ou 2 suivant les cas, \340 vous de pr\351ciser sur vot
re exemple." }}}{EXCHG {PARA 338 "> " 0 "" {MPLTEXT 1 0 169 "graphe1:=
pointplot(\{seq([Tab[i,1],Tab[i,2]],i=1..nb)\}):\ngraphe2:=plot([m[1]+
v[1]*t,m[2]+v[2]*t,t=-6..6],color=blue):\ngraphe3:=plot([x,regression(
x),x=0..10],color=red):\n" }{TEXT -1 45 "Voil\340 ce que cela a donn
\351 dans notre exemple:" }}}{EXCHG {PARA 339 "> " 0 "" {MPLTEXT 1 0 
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