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suivant

5
y−z = 2 −x+3z = 1
(D) : (Δ) :
−x−y +2 = 0 −x−3y = 2
(D) (Δ)
(Δ)
M (Δ) α M (α,y ,z )∈ (Δ)α α α α
P M (D)α α
α α P (Δ)0 α0
P Mα α0 0
4
00 π(E) :y +y =f(x) x∈ [0, ]2
f(x) =x+1
(E)
πy(0) = 0 y( ) = 02
π0y(0) = 0 y ( ) = 0
2
f(x) = (x−1)sinx
2007

14
     
−2 0 0 0 0 0 1 0 0
     A = 2 1 2 N = 2 3 2 I = 0 1 0 .3
0 0 −2 0 0 0 0 0 1
2 2A A = 2I −A3
n∀n∈N,∃(a ,b )∈R, A =a I +b An n n 3 n
a = 2bn+1 n
A
b =a −bn+1 n n
b =−b +2bn+2 n+1 n
1 nb = (1−(−2) )n 3
a b nn n
nA n
2 n+1N N n> 1 :N =
n3N
nN n n > 1
n = 0
A =N −2I3
k=nX
k k n−k n!n k(N −2I ) = C N (−2I ) C =3 3n n k!(n−k)!
k=0
1n n nA = (1−(−2) )N +(−2) I3
3
nA
u = (−1,0,1) v = (−3,2,0) w = (0,1,0)
3B = (u,v,w) R P
B
−1P 
−2 0 0
−1 D = 0 −2 0 A =PDP
0 0 1
 
n(−2) 0 0
n n D = 0 (−2) 0
0 0 1
n n −1 nA = PD P A
n
2007