(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

F = (a, b, c, d) ∈ IR 4 | a + b + c = 0
G = 〈(1, 1, 0, 0), (2, 2, 0, 5), (0, 0, 0, 1)〉
¡ ¨ IR 4
F.
¢
F ∩ G.
¨¥ ¨ (a, b, c, d) ∈ F £¢ c = −a−b
F
¢
F = {(a, b, −a − b, d) | a, b, d ∈ IR}
= {a(1, 0, −1, 0) + b(0, 1, −1, 0) + d(0, 0, 0, 1) | a, b, d ∈ IR}
= 〈(1, 0, −1, 0), (0, 1, −1, 0), (0, 0, 0, 1)〉
¢
§ ¢
1
0
0
1
−1
−1
0
0
((1, 0, −1, 0), (0, 1, −1, 0), (0, 0, 0, 1)) ¡
0 0 0 1
F
G
1
2
1
2
0
0
0
5
0 0 0 1
1 1 0 0
2 2 0 5
0 0 0 1
−−−−−→
ℓ2 − 2ℓ1
−−−−→
ℓ2 − ℓ3
1 1 0 0
0 0 0 5
0 0 0 1
1 1 0 0
0 0 0 1
0 0 0 0
103
¢
¢
−−−−→
1
5 ℓ2
G = 〈(1, 1, 0, 0), (2, 2, 0, 5), (0, 0, 0, 1)〉
= 〈(1, 1, 0, 0), (0, 0, 0, 5), (0, 0, 0, 1)〉
= 〈(1, 1, 0, 0), (0, 0, 0, 1), (0, 0, 0, 1)〉
= 〈(1, 1, 0, 0), (0, 0, 0, 1), (0, 0, 0, 0)〉
= 〈(1, 1, 0, 0), (0, 0, 0, 1)〉
1 1 0 0
0 0 0 1
0 0 0 1