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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 8 "restart;" }
{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 200 "> " 0 "" {MPLTEXT 1 202 18 "produit:=proc(A,B)" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 24 "\n local k,C,n,p,q,i,j,t;" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 33 "\n t:=taille(A); n:=t[1]; p:=t[2];" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n t:=taille(B); q:=t[2];" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 43 "\n if (t[1]<>p) then RETURN(IM
POSSIBLE); fi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n C:=array(1
..n,1..q);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 23 "\n for i from 1 t
o n do " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 23 "\n  for j from 1 to \+
q do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 39 "\n   C[i,j]:=add(A[i,k]
*B[k,j],k=1..p); " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\n  od;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 18 "\nRETURN(evalm(C));" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+
" 0 "" {MPLTEXT 1 202 22 "MatPermut:=proc(i,j,n)" }{MPLTEXT 1 202 0 ""
 }{MPLTEXT 1 202 13 "\nlocal k,l,P;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 22 "\n P:=array(1..n,1..n);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 
23 "\n for k from 1 to n do " }{TEXT 203 1 " " }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 24 "\n  for l from 1 to n do " }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 16 "\n   P[k,l]:=0;  " }{MPLTEXT 1 202 0 "" }{MPLTEXT 
1 202 6 "\n  od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n  P[k,k]:
=1; " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nod; " }{MPLTEXT 1 202 
0 "" }{MPLTEXT 1 202 43 "\n  P[i,i]:=0;P[j,j]:=0;P[i,j]:=1;P[j,i]:=1;"
 }{TEXT 203 2 "  " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(P)
;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 7 "\nend:  " }{MPLTEXT 1 202 
0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 21 "MatDilat:=proc(a
,j,n)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal k,l,P;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n P:=array(1..n,1..n);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 23 "\n for k from 1 to n do " }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 24 "\n  for l from 1 to n do " }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 14 "\n   P[k,l]:=0;" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 6 "\n  od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 13 "\n  P[k,k]:=1;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;"
 }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\n    P[j,j]:=a;" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 10 "\nevalm(P);" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+
" 0 "" {MPLTEXT 1 202 27 "MatTransvect:=proc(i,a,j,n)" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 13 "\nlocal k,l,P;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 22 "\n P:=array(1..n,1..n);" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 23 "\n for k from 1 to n do " }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 24 "\n  for l from 1 to n do " }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 14 "\n   P[k,l]:=0;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 6 "\n  od;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\n  P[k,k]:=1
;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 ""
 }{MPLTEXT 1 202 13 "\n  P[i,j]:=a;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 10 "\nevalm(P);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }
{MPLTEXT 1 202 0 "" }}}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 13 "Exercic
e 2bis" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 
0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG 
{PARA 203 "" 0 "" {TEXT 206 144 "Etant donn\351 que les op\351rations \+
\351l\351mentaires s'obtiennent par produit de la matrice initiale par
 des matrices \351l\351mentaires d\351j\340 construites on a:" }{TEXT 
205 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 207 11 "question a)" }
{TEXT 205 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 205 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 24 "\nB:=MatPermut(i,j,t[1]);" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 22 "\n evalm(Produit(B,A));" }{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 208 
11 "question b)" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 24 "Dilat_ligne:=proc(a,i,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 23 "\nB
:=MatDilat(a,i,t[1]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n eva
lm(Produit(B,A));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }
{MPLTEXT 1 202 0 "" }}{PARA 204 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {TEXT 208 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 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 29 "\nB:=MatTransvect(i,a,j,t[1]);" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\n evalm(Produit(B,A));" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 6 "\nend: " }{MPLTEXT 1 202 0 "" }
}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 203 "
" 0 "" {TEXT 207 11 "question e)" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 
"> " 0 "" {MPLTEXT 1 202 27 "Permut_colonne:=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 24 "\nB:=MatPermut(i,j,t[1]);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 22 "\n evalm(Produit(A,B));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 
6 "\nend: " }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 0 "" }}}{PARA 205 "" 0 "" {TEXT 209 0 "" }}{PARA 205 ""
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