(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

106 CAPÍTULO 9. £¡ §© ¢¦£ ¤ ¢¥ § ¡
α, Fα
¢ ¢ α, Fα.
G = 〈(1, 1, 0), (0, 0, 2)〉 .
¢ ¢ α, dim (G + Fα) .
¡ IR 3 .
¢ ¢ α, G + Fα.
¨ ¢ α Fα
¡
¨¥
IR 3
¡
α = 0
£¢
F0 = (x, y, z) ∈ IR 3 | x = 0 = {(0, y, z)} = {y(0, 1, 0) + z(0, 0, 1)}
= 〈(0, 1, 0), (0, 0, 1)〉
Fα = {(x, y, z) | x = αy y = z} = {(αy, y, y)} = 〈(α, 1, 1)〉
dim F0 = 2
α = 0
1
0 ¢ ¢
dim Fα = α = 0
α = 1
0
0
1
0
1
0
2
0
1 1 0
0 0 2
0 1 0
0 0 1
−−−−−→
ℓ2 ↔ ℓ1
−−−−→
ℓ1 − ℓ2
1 1 0
0 1 0
0 0 2
0 0 1
1 0 0
0 1 0
0 0 1
0 0 0
−→
1
2 ℓ3
1 1 0
0 1 0
0 0 1
0 0 1
−−−−→
ℓ3 − ℓ4
G + F0 = 〈(1, 0, 0), (0, 1, 0), (0, 0, 1)〉
dim (G + F0) = 3
1 1 0
0 1 0
0 0 1
0 0 0
0 0 1
α = 0 ¢ ¢ α 1 1
1 1 0
0 0 2