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{SECT 0 {EXCHG {PARA 259 "" 0 "" {TEXT 269 79 "Compl\351ment  6b - Ava
ntage de la m\351thode d'\351limination de Gauss : \311tude d'un cas" 
}}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 52 "Par Claude St-Hilaire, claude
.sthilaire@videotron.ca" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "
restart: with(linalg):" }}}{PARA 0 "" 0 "" {TEXT -1 89 "Pour quelles v
aleurs de a et b, le syst\350me d'\351quations suivant n'a-t-il pas de
 solution ?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "eq1:=x+2*y+a*
z=4;\neq2:=2*x-y+3*z=b;\neq3:=3*x-4*y+2*z=-3;" }}}{SECT 1 {PARA 257 "
" 0 "" {TEXT -1 14 "La r\351ponse de " }{TEXT 260 5 "solve" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "solution1:=solve(\{eq1,eq2,eq3\},\{
x,y,z\});" }}}{PARA 0 "" 0 "" {TEXT -1 116 "Pour a = 4, le d\351nomina
teur s'annule. Affirmer que pour a = 4, le syst\350me n'a pas de solut
ion, quelque soit b, est  " }{TEXT 256 6 "FAUX. " }{TEXT -1 20 "Cherch
ons pourquoi? " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 258 "" 0 "" {TEXT -1 16 "La r\351ponse avec " }{TEXT 
257 8 "linsolve" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=matrix
(3,3,[1,2,a,2,-1,3,3,-4,2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "v:=matrix(3,1,[4,b,-3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "solution2:=linsolve(A,v);" }}}{PARA 0 "" 0 "" {TEXT -1 43 "La \+
solution1 est la m\352me que la solution2. " }}}{SECT 1 {PARA 3 "" 0 "
" {TEXT 267 17 "La solution avec " }{TEXT 256 9 "gausselim" }{TEXT 
268 21 ", la m\351thode de Gauss" }{TEXT -1 1 " " }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "B:=augment(A,v);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "gausselim(B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 53 "La r\351ponse : Le syst\350me
 n'a pas de solution si a = 4 " }{TEXT 258 22 "et b diff\351rent de 1/
2." }}{PARA 0 "" 0 "" {TEXT -1 15 "Dans le cas o\371 " }{TEXT 259 16 "
a = 4 et b = 1/2" }{TEXT -1 106 ", on a un syst\350me compatible avec \+
une variable libre. Ainsi il y a une infinit\351 de solutions. V\351ri
fions : " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "subs(\{a=4,b=1/2
\},\{eq1,eq2,eq3\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sol
ve(%,\{x,y,z\});" }}}{PARA 0 "" 0 "" {TEXT -1 73 "Lorsque a = 4 et b =
 1/2, chaque num\351rateur et chaque d\351nominateur de la " }{TEXT 
261 9 "solution1" }{TEXT -1 122 " est nul, alors le syst\350me d'\351q
uations est \351quivalent  0x = 0, 0y = 0 et 0z = 0 lequel poss\350de \+
une infinit\351 de solutions. " }}{PARA 0 "" 0 "" {TEXT -1 61 "V\351ri
fions que chaque num\351rateur \351gale 0 si a = 4 et b = 1/2 :" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "numerateur1:=numer(rhs(solu
tion1[1]));numerateur2:=numer(rhs(solution1[2]));numerateur3:=numer(rh
s(solution1[3]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "subs(
\{a=4,b=1/2\},[numerateur1,numerateur2,numerateur3]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
266 10 "Conclusion" }}{PARA 0 "" 0 "" {TEXT -1 63 "Pour \351tudier la \+
consistance d'un syst\350me d'\351quations lin\351aires " }{TEXT 262 
15 "avec param\350tres" }{TEXT -1 3 " : " }}{PARA 0 "" 0 "" {TEXT 263 
60 "Trouvez la matrice \351chelonn\351e avec gausselim et interpr\351t
er." }{TEXT -1 88 " Ne pas r\351soudre : ni avec, gausselim avec backs
ub, ni gaussjord, ni linsolve, ni solve." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }{TEXT 264 120 "Interpr\351tez la matrice \351chelonn\351e, (fair
e une \351tude particuli\350re pour des valeurs qui annulent un ou des
 d\351nominateurs)." }{TEXT 265 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
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