(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

¤ α2
= 0 ¡
M0
M0 = {X ∈ M3×1(IR) | (A + 0I3) X = 0}
= ∈ M3×1(IR) |
a
b
c
2 −1 1
4 −3 1
4 −3 1
−−−−→
ℓ3 − ℓ2
2 −1 1
4 −3 1
0 0 0
2 −1 1
4 −3 1
4 −3 1
¤ AX = 0 ©
M0 =
=
=
a
b
c
a
b
c
a
b
c
M0 =
=
a
b
c
=
0
0
0
2 −1 1
−−−−−→
ℓ2 − 2ℓ1 0 −1 −1
0 0 0
∈ M3×1(IR) | 2a − b + c
= 0 − b − c = 0
∈ M3×1(IR) | 2a − 2b
= 0 b = −c
∈ M3×1(IR) | a = b = −c
a
a
−a
1
1
−1
| a ∈ IR
M0 ¢
¤ α3
=
1
M−2
M−2 = {X ∈ M3×1(IR) | (A + 2I3) X = 0}
= ∈ M3×1(IR) |
4 −1 1
4 −1 1
4 −3 3
a
b
c
−−−−→
ℓ2 − ℓ1
4 −1 1
0 0 0
4 −3 3
4 −1 1
4 −1 1
4 −3 3
4 −1 1
−−−−→
ℓ3 − ℓ1 0 0 0
0 −2 2
1
−1
(0) = dim M0 = 1
= −2 ¡
a
b
c
¤ (A + 2I3)X = 0 ©
=
0
0
0
4 −1 1
−−−−−→
ℓ2 ↔ ℓ3 0 −2 2
0 0 0
183