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TSI2
no7
3J=
021
0−1 2
010
fR3JR3
a3
Ma=
a2 1
0a−1 2
0 1 a
J
χJ(x) =
x−2−1
0x+ 1 −2
0−1x
=
x−a−3−1
0x−1−2
0x−1x
(C2+C3)
=
x−3−1
0x−1−2
0 0 x+ 2
(L3−L2)
χJ(x) = x(x−1)(x+ 2)
Spec(J) = {0,1,−2}
E0= Vect{(1,0,0)}
E1
J−I
x
y
z
=
0
0
0
⇐⇒ 
−x+ 2y+z= 0
−2y+ 2z= 0
y−z= 0
⇐⇒ y=z x = 3y
E1= Vect{(3,1,1)}
E−2
J−I
x
y
z
=
0
0
0
⇐⇒ 
2x+ 2y+z= 0
y+ 2z= 0
y+ 2z= 0
⇐⇒ y=−2z x =3
2z
E−2= Vect{(3,−4,2)}

J
J=P DP −1D=
0 0 0
0 1 0
0 0 −2
P=
1 3 3
0 1 −4
0 1 2
Ma=J+aI =P DP −1+aP IP −1=P(D+aI)P−1
Ma=P DaP−1Da=
a0 0
0 1 + a0
0 0 a−2
Ma0Da
a6= 0 a6=−1a6= 2
Maa∈R\ {0,−1,2}
a X X2=Ma
a X 3
X2=Ma
XMa=XX2=X3=X2X=MaX
X Ma
J=Ma−aI
XJ =X(Ma−aI) = XMa−aX =MaX−aX = (Ma−I)X
X J
hR3X
R3
f h
x f λ ∈Rf(x) = λx
f(h(x)) = h(f(x)) = h(λx) = λh(x)
h(x)Eλ
1µ∈R
h(x) = µx x h
f h
f
h
h
P X
∆ 3 X=P∆P−1

TSI2
Ma=X2=P∆P−1P∆P−1=P∆2P−1P∆2P−1=P DaP−1
P−1P
∆2=Da
Da
a, 1 + a−2 + a
a>2
a>2
∆ = 
√a0 0
0√1 + a0
0 0 √a−2
, X =P∆P−1.
X2=P∆2P−1=P DaP−1=Ma
a2
X3X2=Ma
a X
X2=Ma[2,+∞[