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{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 1 "\n" }}}{SECT 1 {PARA 201 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 15 "taille
:=proc(A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n local t,u,n,p;"
 }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n   t:=[op(2,evalm(A))];" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n   n:=op(2,t[1]);p:=op(2,t[2
]); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\n   [n,p];" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}}{EXCHG 
{PARA 202 "" 0 "" {TEXT 203 10 "Exercice 2" }{TEXT 204 0 "" }}}{EXCHG 
{PARA 203 "" 0 "" {TEXT 205 11 "question a)" }{TEXT 204 0 "" }}}
{EXCHG {PARA 203 "" 0 "" {TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 25 "Permut_ligne:=proc(i,j,A)" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 13 "\nlocal B,k,t;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 14 "\nt:=taille(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB:
=array(1..t[1],1..t[2]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB
:=evalm(A);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 t
o t[2] do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 35 "\n B[i,k]:=A[j,k];
 B[j,k]:=A[i,k];  " }{TEXT 206 21 "on ne modifie que la " }{TEXT 207 
23 "i-eme et j-eme  lignes " }{TEXT 206 4 "de B" }{MPLTEXT 1 202 0 "" 
}{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\ne
valm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }{MPLTEXT 
1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}
{EXCHG {PARA 200 "> " 0 "" {TEXT 207 11 "question b)" }{MPLTEXT 1 202 
0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "Dilat_ligne:=pro
c(a,i,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal k,t,B;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 27 "\nB:=array(1..t[1],1..t[2]);" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 13 "\nB:=evalm(A);" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 24 "\nfor k from 1 to t[2] do" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 21 "\n B[i,k]:=a*A[i,k];  " }{TEXT 206 21 "on ne modifi
e que la " }{TEXT 207 12 "i-eme ligne " }{TEXT 206 4 "de B" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }
{MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {TEXT 207 11 "question c)" }{MPLTEXT 1 202 0 "" }}
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "Transvect_ligne:=proc(i
,a,j,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal k,t,B;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 27 "\nB:=array(1..t[1],1..t[2]);" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 13 "\nB:=evalm(A);" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 24 "\nfor k from 1 to t[2] do" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 28 "\n B[i,k]:=A[i,k]+a*A[j,k];  " }{TEXT 206 21 "on ne
 modifie que la " }{TEXT 207 12 "i-eme ligne " }{TEXT 206 4 "de B" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 10 "\nevalm(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 
5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" 
}}}{EXCHG {PARA 200 "> " 0 "" {TEXT 207 11 "question d)" }{MPLTEXT 1 
202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "CherchePivot
_colonne:=proc(A,i)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 12 "\n local
 t,k;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 16 "\n  t:=taille(A);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 46 "\n  if is(i>t[1])then RETURN(I
MPOSSIBLE); fi;  " }{TEXT 206 42 "la proc\351dure ne fonctionne que si
 l'indice" }{TEXT 207 39 " i ne d\351passe pas le nombre de colonnes" 
}{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 26 "\n  for k from i to t[1] do" 
}{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 40 "\n   if is(A[k,i]<>0) then RE
TURN(k); fi;" }{TEXT 207 8 " renvoi " }{TEXT 206 10 "le premier" }
{TEXT 207 8 " indice " }{TEXT 206 19 "correspondant \340 un " }{TEXT 
207 18 "coefficent non nul" }{TEXT 206 1 " " }{TEXT 207 24 "\340 parti
r de aii dans la " }{TEXT 207 9 "colonne i" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 6 "\n  od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\n
  RETURN(0);" }{TEXT 206 1 " " }{TEXT 207 14 "sinon renvoi 0" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}
{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 203 "" 0 "" 
{TEXT 205 11 "question e)" }{TEXT 204 0 "" }}}{EXCHG {PARA 203 "" 0 ""
 {TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 27 "Permu
t_colonne:=proc(i,j,A)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nloc
al B,k,t;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\nt:=taille(A);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 27 "\nB:=array(1..t[1],1..t[2]);" 
}{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nB:=evalm(A);" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 24 "\nfor k from 1 to t[1] do" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 35 "\n B[k,i]:=A[k,j]; B[k,j]:=A[k,i];  " }
{TEXT 206 21 "on ne modifie que la " }{TEXT 207 25 "i-eme et j-eme  co
lonnes " }{TEXT 206 4 "de B" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "
\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(B);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }{MPLTEXT 1 202 0 "" }
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