(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

162 CAPÍTULO 14. ¦£¦£ ££
¤
A
¡
pA(x) = det (A − xI3) =
= (2 − x)
3 − x 2
−1 2 − x
2 − x 1 0
2 3 − x 2
0 −1 2 − x
−
2 2
0 2 − x
= (2 − x)(3 − x)(2 − x) + 2(2 − x) − 2(2 − x)
= (2 − x) 2 (3 − x)
= 2 α2
¢
§ £ ¡ ¢ ¤£¦¥ § ¢ ©¨
¤ A ¢ α1 = 3
¢ ¡
(2) 2 = (3) =
1
¤ α1
M2
M2 = {X ∈ M3×1(IR) | (A − 2I3) X = 0}
= ∈ M3×1(IR) |
=
=
=
a
b
c
a
b
c
a
b
c
0 1 0
2 1 2
0 −1 0
= 2 ¡
a
b
c
=
0
0
0
∈ M3×1(IR) | b
= 0 2a + b + 2c = 0
a
0
−a
=
∈ M3×1(IR) | b
= 0 a + c = 0
1
∈ M3×1(IR) | a ∈ IR = 0
−1
¢
¤
1
0
−1
α2
M2
M3 = 3 ¡
M3 = {X ∈ M3×1(IR) | (A − 3I3) X = 0}
= ∈ M3×1(IR) |
=
=
a
b
c
a
b
c
a
b
c
∈ M3×1(IR) |
−1 1 0
2 0 2
0 −1 −1
1 −1 0
1 0 1
0 1 1
(2) = dim M2 = 1
a
b
c
∈ M3×1(IR) | a = b = −c
a
b
c
=
=
0
0
0
0
0
0