(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

−−−−→
ℓ1 − ℓ3
1 1 −1 0
0 0 1 0
0 0 0 1
0 0 0 0
−−−−→
ℓ1 + ℓ2
1 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
((1, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1))
¡ F
¢ ¢
1 1 −1 1
1 0 1 −1
1 −1 −4 4
1 1 −1 1
1 0 1 −1
1 −1 −4 4
−−−−→
ℓ3 − ℓ1
−−−−−→
ℓ3 − 2ℓ2
−−−−−→
ℓ2 − 2ℓ3
−−−−→
ℓ1 + ℓ3
1 1 −1 1
1 0 1 −1
0 −2 −3 3
1 1 −1 1
0 −1 2 −2
0 0 −7 7
1 1 −1 1
0 −1 0 0
0 0 1 −1
1 1 0 0
0 1 0 0
0 0 1 −1
−−−−→
ℓ2 − ℓ1
−−−−−→
− 1
7 ℓ3
−−−−−→
−ℓ2
−−−−→
ℓ1 − ℓ2
1 1 −1 1
0 −1 2 −2
0 −2 −3 3
1 1 −1 1
0 −1 2 −2
0 0 1 −1
1 1 −1 1
0 1 0 0
0 0 1 −1
1 0 0 0
0 1 0 0
0 0 1 −1
((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, −1, 1))
¡ G
(a, b, c, d) ∈ F ∩ G£¢ (a, b, c, d) ∈ F (a, b, c, d) ∈ G
⇐⇒
¡
(a, b, c, d) = α(1, 1, 0, 0) + β(0, 0, 1, 0) + γ(0, 0, 0, 1)
(a, b, c, d) = α(1, 0, 0, 0) + β(0, 1, 0, 0) + γ(0, 0, −1, 1)
(a, b, c, d) = (α, α, β, γ)
(a, b, c, d) = (α, β, −γ, γ)
=⇒
a = b
c = −d
F ∩ G = {(a, a, −d, d) | a, d ∈ IR}
= {a(1, 1, 0, 0) + d(0, 0, −1, 1) | a, d ∈ IR}
= 〈(1, 1, 0, 0), (0, 0, −1, 1)〉
¡ ¨ IR 3¡
Fα = (x, y, x) ∈ IR 3 | x = αy = αz
105
α ∈ IR