(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

(a, b, c, d) = (a, b, b, 0)
H = 〈(1, 0, 0, 3), (2, 0, 0, 1)〉
= 〈(1, 0, 0, 3), (0, 0, 0, −5)〉
= 〈(1, 0, 0, 3), (0, 0, 0, 1)〉
= 〈(1, 0, 0, 0), (0, 0, 0, 1)〉
(a, b, c, d) ∈ G ∩ H£¢ (a, b, c, d) ∈ G (a, b, c, d) ∈ H
¢¡
(a, b, c, d) = α(1, 0, 0, 0) + β(0, 0, 0, 1) = (α, 0, 0, β)
G ∩ H = {(a, 0, 0, 0) | a ∈ IR} = 〈(1, 0, 0, 0)〉
¡ ¨ IR 4
=⇒
F = (a, b, c, d) ∈ IR 4 | a = 0 c = 2b
G = 〈(1, −1, 0, 2), (−1, 2, 0, 1), (2, −3, 0, 1)〉
dim F = dim G = 2.
F ∩ G.
b = c
d = 0
¨¥ ¨ (a, b, c, d) ∈ F£¢ a = 0 c = 2b
F
¢
F = {(0, b, 2b, d) | b, d ∈ IR}
= {b(0, 1, 2, 0) + d(0, 0, 0, 1) | b, d ∈ IR}
= 〈(0, 1, 2, 0), (0, 0, 0, 1)〉
¢
§ ¢ ¡
0 1 2 0
0 0 0 1
((1, 1, 0, 0), (0, 0, 1, 0)) F dim F = 2
b = 0
¢ ¢
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