c         R   c     R   c  

 
    c         R   c     R   c                  X c                 R   Y     ! #"%$#&')(#*+-,/. fL):$D9*#M9;' L4< E @# 87)+- $c9H+ ):$ 46!3(* @+ ):$X)i$E12$ E.%,/#f!KJ (%57 L E4+ ) $D4<) (%L4 @#%$D!KJ +- @! E# N !3#M6n[\+ @,/# A⃗ x = ⃗ b. 0  Q}[1 wG9*4 A #%$ `)# N ×N ,L E @49*#D @(*?-4<.% E#D!KJ +- @! E# N !#c9*+2#Hƒq9H4#*)7 @$ aij 8 1 ≤i, j ≤N 8 !+ ))(0$*8 ⃗ b #%$ g ) O #09s @#* M9H+-<+-))#TV N 9H+-,Ta+-$@L)7 @#%$ bj 8 1 ≤j ≤N 8K!3+ )) (*#%$f#* ⃗ x #%$ f ) O #09s E#% g9H+ + ) )#jV N 9H+ ,/a+-$@L)7 E#0$ xj 8 1 ≤j ≤N 8a4<):9H+ ) )7 #%$%Q fL) $"6 $E4< E#-8)+ :$c3 E4<46$E+ ) $R#%$c) +L @L E4+ ) $c,L E @49*4<#%<#%$R$ @ ) !L ;!$%824eQ # Q A =      a11 a12 · · · a1N a21 a22 · · · a2N Q Q Q Q Q Q Q Q Q aN1 aN2 · · · aNN     , ⃗ b =      b1 b2 Q Q Q bN     , ⃗ x =      x1 x2 Q Q Q xN     . P#M$ 13$ E.*,/# 0 :Q<}21Ca#*3 Rb* E @#"(09H @4Y c#HI349*4Y @#*,/#*)7 &$E+  $D6B[\+- E,/#g!KJ  )r$E12$ E.%,/#f!3# N (057 U @4<+-) $RV N 4) 9*+ ))2#0$ x1, x2, . . . , xN *          a11x1 + a12x2 + · · · + a1NxN = b1, a21x1 + a22x2 + · · · + a2NxN = b2, Q Q Q aN1x1 + aN2x2 + · · · + aNNxN = bN. 0  Q7/31 23} 2L/ 

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%#@')#&B%C_UW&  E @FACBDPYH<KJNQP RZP=L BMAVU J A J > L L BMAVP=E 3< NQPFACBDJ> < ` \BMAVJ < BDJ BDJ > ` J U L A =J RZJEKL L BMAVP=E 3< NQPFACBDJSACE  \BMAVJ< BDJ Y>MA aij = 0 ` :=< B;L :F< L U :F< ` NQJ i, j L JN H <KJ 1 ≤j < i ≤N BDJ > ` b 1 ≤i < j ≤N  b ;>=
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b  JM>ML < E9> 2> L RSJ LTBMAVPFE 3< NQP=ACB]J >M< ` \ BMAVJ< B BDJ > ` b L BMAVP=E 3< NQPFACBDJ;ACE  \BMAVJ < B  b 2 :+7$ +-) $T) 4) $ @L)7 57#r6y,/L E @49*# A $ +-4Y T E @46L)?- 4< @#u$Ea(* @4<#% E#-Q 9&+ :$ 9*+ ) $ @L E+ ):$AL+ ;$&57#n<#/!3(H @#* @,/4<)  )7 "!3# A #%$ "#T E+3!3 4Y g!3#%$ O L#* ;$A!346L?-+ )  <#0$ aii #H %8` 4$@57#i,U @ E469H# A #%$ q$  :+7$ (%#i E(%? 4<.% E#-8) +  $ O + ) $ aii ̸= 0 8 i = 1, 2, . . ., N Q%dA4<):$ 4W8%574< @#SVR!34 O 4$E#* P9;': 57#`(%57 L E4+ )B!3# 0  Q7/31Z:L F#` E#% E,/#X!4 ? + ):LW8 4C)FJ #%$ M  $g @#%$ E @49H E4<[D!3#q$Ea+-$E#* M57# aii = 1 8 i = 1, 2, . . . , N Q " ) $B9H#9% $%8K ,U @ E469H# A #%$ C E @46L)?- 4< @#R$  :(% E4#* @#A O #%9c!3#%$ O L#* ;$R}A! ) $X$@M!346L?-+ )  <#R#* %8-!# 0  Q7/31s8Z)+- $g!3(%!4$E+ ):$f$E 9%9H#%$@$E4 O #*,/#*)7 g<#0$"4) 9*+ ))2#0$ xN, xN−1, . . . , x1 QZ{C) #HhZ#H %8 )+- $R O +-) $ * xN = bN #* &:+- i = N −1, N −2, . . . , 3, 2, 1 * xi = bi − N X j=i+1 aijxj. 0 :Q 171 fL) $A<#n9* $A+34>6,U @ E469H# A #%$ " @(*?  <4.* @#g,/ 4$A)+ )>) (%9H#0$E$@L4 @#*,/#*)7 R E @46L)?- 4< @# $Ea(* @4<#% E#-86o,/(* E'+3!3#i!KJ (*4<,/4) U @4<+-) !3#[]gL $@$n  ;>:+- T=3 !3#u @ @ ) $ [\+ @,T#% #r$E13$G @.*,/# A⃗ x = ⃗ b #%) ) $E13$G @.*,/#q(05- 4 O L#*)7 0 9LJ #%$ NxVUNx!34 E#a+-$@$E(%! )- n ,Tb%,/# $E+ 3 E4+ ) 1C @ E46L) ? 6L4 E#g$E:(% E4#* & O #%9f!3#0$ O  <#% ;$g}g$E R6/!34 ? +-) L# Q    *  ,/ )O  #.  "# O" & "Y . Z.-, $ * . ]S+ ):$ 46!3(* @+ ):$&)o#*I3#*,/#n O #09 N = 3 a+  f,/+ )7 E @#* A9*+ ,/,/#*)7 A[  4< @#j6/ @ @ ) $GN [\+- E,U @4<+-)n!KJ )/$ 13$ E.%,T#c4<) (%L4 @#S#%)n)/$E12$ E.%,/#X @ E46L)?-6L4 E#D$ a(* @4#* _(%574 O L#*)7 %Q fL) $R9*#H &#*I2#%,/<#-8)+- $R9;'+ 46$E4$@$ +-) $+* A =   4 8 12 3 8 13 2 9 18  , ⃗ b =   4 5 11  . P#g$E13$G @.*,/# A⃗ x = ⃗ b !3# O 4#*)7 A!L):$R9H#M9*-$ *    4x1 + 8x2 + 12x3 = 4, 3x1 + 8x2 + 13x3 = 5, 2x1 + 9x2 + 18x3 = 11. 0 :Q ?1   #&* =L'),-+l Pf @#*,/4<.% E#D+ a(* ;U @4<+-)n9*+ ) $E4$ E#RVg!34 O 4$E#* _6" E#%,T4.* @#c(%57 L E4+ ) !3# 0  Q 71S  a11 = 4 0 La#*(M @#*,/4<#% c4 O +L M1D:+- R+ =3 @#*)4 * x1 + 2x2 + 3x3 = 1. 0 :Q 251  


 %4 1 
  2K1 {X) $  4Y @#")+- $D$ +- $G @ @^1-+ ) $ 3 [\+ 46$XWJ (%57 U @4<+-) 0 :Q 251CVM6j!#*3I34.*,/#A(05-:U E4+ )r!3# 0  Q 71 #* 2 [\+-4$/WJ (%57 U @4<+-) 0  Q7231nVy E @+ 46$E4<.%,T#v(%57 L E4+ )~!3# 0 :Q ?1sQ 9&+- $/+ =3 @#*)+-) $T) $E13$G @.*,/#M(%574 O L#*)7 &V 0  Q 71D574F#0$G 0 #*)i @(*a(H @ )7 0  Q7231D1 *    x1 + 2x2 + 3x3 = 1, 2x2 + 4x3 = 2, 5x2 + 12x3 = 9. 0  Q 551 9A+  $c+-= $E#* O + ):$X57#g<#0$R!3#*Ir!3#* @)4.* @#%$S(%57 L E4+ ) $c!3# 0 :Q 571X[\+ )7 c   @  @ E#f$ #%<#*N ,/#%)- j!#*3I4<) 9*+ ))2#0$ x2 #* x3 0 eJ 4<):9H+ ) )7 # x1 v(H @((*4<,/4)(*#21f#H B)+- $g:+- O +-) $ @#%9*+ ,/,/#*) 9*#* R#g E+39*(%!3(g#*)i6L46$E$@L)7 c4<):9;' L)?-(*#f/ E#%,T4.* @#f(%57 U @4<+-)FQ ;> De# =*'.,A+l 9&+- $o!34 O 4$E+ ):$i !3#%3I34<.%,/#p(%57 U @4<+-) !# 0  Q 551v:L 2 0 # !#*3I34.*,/#M4 O +L M1sQS9A+  $c+-=3 E#%)+ ):$ * x2 + 2x3 = 1. 0 :Q7431 9A+  $"$ +- $ E ;^1 + ):$ 5 [\+-4$ 0  Q 4F1cV/6T E @+ 46$ 4.*,/#M(05-:U E4+ )i!3# 0  Q 551D#* A)+ :$c+ =3 @#*)+-) $ #B$E12$ E.%,/#g$E4 O L)7 *    x1 + 2x2 + 3x3 = 1, x2 + 2x3 = 1, 2x3 = 4, 0  Q 851 574P#%$ &(%574 O  <#%)7 R v$E13$G @.*,/# 0 :Q ?1sQ ;> *%U#L c=*'),-+l |4)  <#%,T#%)7 %84F$ ƒT A!#B!34 O 46$ #% Rn @ E+-4$E4<.%,/#f(057 U @4<+-)r!3# 0  Q 851 :L R#g E @+ 46$ 4.*,/#g4 O +L 08574K#%$ &#*) 9*+ @#"469H4 2 83a+  &+-=3 E#%)4 *    x1 + 2x2 + 3x3 = 1, x2 + 2x3 = 1, x3 = 2. 0  Q 651 "# 0  Q 651H84<#%$ &[  9*4<#j!3#n!3(%!3 4< @#j$E 9*9*#%$@$ 4 O #%,T#%)7 c#%$A4<):9H+ ) )7 #%$ x3, x2, x1 9H+ ,/,/# ) +  $RWJ  O + ):$S!3(09H @4Y A! L) $ 0  Q 151sQA9A+  $&+ =3 @#*)+-) $ * x3 = 2, x2 = −3, x1 = 1. Y * )& M #,/.   *  ,/ )O  9A+  $A @(%$E#*)7 E+-) $c,L4)- @#*)  )7 A)oL? +- E4< E' ,T#M574W8 #*ha#09s E (j  &)>+ ;!34) U @#* 08 a#* @,/#H M!3#j @(% <46$E#* &WJ (%<4,/4<):U E4+ )y!3+ )7 "#j,/(09*L) 4$E,/#nq(* E(T!3(%9* E4< f! ) $"q$E#%9H E4+ )  E(09H(%!#*)7 E#-QPm_+  n E(0L4$E#* n9H#H T+ =3zG#09s @4Y[G8k)+ :$jL :#%<+-) $ A(i) 6>,U @ E469H#u#H ⃗ b(i) # $E#%9*+ ) !r,/#*,n= E#M+-=3 E#%)2 $R O L)7 D6 i NW4.*,/#g(H ;La#M!3#MeJ (*4,T4) L E4+ )FQ dA4<):$ 4F#f @ =<#0L 2L 

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A(i) /6j[\+- E,/#M$E4 O  )- @#* A(i) =             uploads/s1/ cours-ingenierie-du-calcul-l3info.pdf

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• Publié le Mai 19, 2022
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