(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

¤ A ¢ α1 = −4
¢ ¡
(4) 2 = (−4) =
1
= 4 α2
¤ α1
M4
M4 = {X ∈ M3×1(IR) | (A − 4I3) X = 0}
= ∈ M3×1(IR) |
a
b
c
0 1 2
3 −8 0
− 3
2 4 0
−−−−−→
ℓ1 ↔ ℓ3
0 1 2
3 −8 0
− 3
2 4 0
− 3
2 4 0
3 −8 0
0 1 2
= 4 ¡
a
b
c
¤ (A − 4I3) X = 0 ©
M4 =
=
a
b
c
8
3 b
b
− b
2
=
M4
−−−−→
ℓ1 + ℓ2
−3 8 0
0 0 0
0 1 2
=
0
0
0
−3 8 0
−−−→
2ℓ1 3 −8 0
0 1 2
−−−−−→
ℓ2 ↔ ℓ3
−3 8 0
0 1 2
0 0 0
∈ M3×1(IR) | −3a + 8b
= 0 b + 2c = 0
| b ∈ IR
=
8
3
1
− 1
2
8
3
1
− 1
¢
¤
2
α2
M−4
M−4 = {X ∈ M3×1(IR) | (A + 4I3) X = 0}
= ∈ M3×1(IR) |
=
=
a
b
c
a
b
c
a
b
c
8 1 2
3 0 0
− 3
2 4 8
(4) = dim M4 = 1
= −4 ¡
a
b
c
=
∈ M3×1(IR) | a =
b + 2c = 0
0
4b + 8c = 0
0
0
0
∈ M3×1(IR) | a
= 0 b + 2c = 0
155