(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

¢ M1
¤ α2
M1 = {X ∈ M3×1(IR) | (A − I3) X = 0}
a
= b ∈ M3×1(IR) |
2 2 0 | 0
−4 −4 0 | 0
4 2 −2 | 0
c
2 2 0
−4 −4 0
4 2 −2
¤ (A + I3) X = 0 ©
M1 =
=
=
−−−−−→
2ℓ1 + ℓ2
a
b
c
a
b
c
−−−−−→
ℓ2 ↔ ℓ3
a
−a
a
=
M1
¢
2 2 0 | 0
0 0 0 | 0
4 2 −2 | 0
2 2 0 | 0
0 0 0 | 0
0 −2 −2 | 0
a
b
c
−−−−−→
ℓ3 − 2ℓ1
−−−−−→
1
2 ℓ1
− 1
2 ℓ3
=
= 1 ¡
0
0
0
2 2 0 | 0
0 0 0 | 0
0 −2 −2 | 0
∈ M3×1(IR) | a + b = 0 b + c = 0
∈ M3×1(IR) | a = c = −b
1
−1
1
| a ∈ IR
(−1) + ¢
¢
(1) = 2 + 1 = 3
1 1 0 | 0
0 0 0 | 0
0 1 1 | 0
(1) = dim M1 = 1
A
¡ ¢ ¨ ¢ ¥¤
P M3×3(IR) ¨
∈
P −1 AP =
¤
α1 0 0
0 α1 0
0 0 α2
=
−1 0 0
0 −1 0
0 0 1
¡ P 1
−2
0
0
1
−1
0 1 1
−1 0 0
0 −1 0
0 0 1
−1 2
P AP =
−1 0 0
0 −1 0
0 0 1
=
1 0 0
0 1 0
0 0 1
= I3
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