(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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104 CAPÍTULO 9. £¡ §© ¢¦£ ¤ ¢¥ § ¡<br />
(a, b, c, d) ∈ F ∩ G£¢ (a, b, c, d) ∈ F (a, b, c, d) ∈ G<br />
¢¡<br />
<br />
<br />
(a, b, c, d) = (a, b, −a − b, d)<br />
<br />
=⇒<br />
⎧<br />
⎨<br />
⎩<br />
dim F ∩ G = 1<br />
(a, b, c, d) = α(1, 1, 0, 0) + β(0, 0, 0, 1) = (α, α, 0, β)<br />
a = α<br />
b = α<br />
c = −a − b = 0<br />
=⇒<br />
⎧<br />
⎨<br />
⎩<br />
a = b<br />
a = −b<br />
c = −a − b<br />
=⇒<br />
F ∩ G = {(0, 0, 0, d) | d ∈ IR} = 〈(0, 0, 0, 1)〉<br />
<br />
¡ ¨ IR 4 <br />
⎧<br />
⎨<br />
<br />
F = 〈(1, 1, −1, 1), (2, 2, 3, −1), (3, 3, 7, −3), (0, 0, 0, 1)〉<br />
G = 〈(1, 1, −1, 1), (1, 0, 1, −1), (1, −1, −4, 4)〉<br />
<br />
F.<br />
<br />
<br />
G.<br />
F ∩ G.<br />
⎩<br />
a = 0<br />
b = 0<br />
c = 0<br />
¨ ¢ ¨¥ 1<br />
2<br />
1<br />
2<br />
−1<br />
3<br />
1<br />
−1<br />
3 3 7 −3<br />
0 0 0 1<br />
1 1 −1 1<br />
2 2 3 −1<br />
3 3 7 −3<br />
0 0 0 1<br />
<br />
−−−−−→<br />
ℓ3 − 3ℓ1<br />
−−−−−→<br />
ℓ3 − 2ℓ2<br />
−−−−−→<br />
ℓ2 + 3ℓ3<br />
1 1 −1 1<br />
2 2 3 −1<br />
0 0 10 −6<br />
0 0 0 1<br />
1 1 −1 1<br />
0 0 5 −3<br />
0 0 0 0<br />
0 0 0 1<br />
1 1 −1 1<br />
0 0 5 0<br />
0 0 0 1<br />
0 0 0 0<br />
<br />
<br />
<br />
−−−−−→<br />
ℓ2 − 2ℓ1<br />
−−−−−→<br />
ℓ4 ↔ ℓ3<br />
−−−−−→<br />
1<br />
5 ℓ2<br />
<br />
1 1 −1 1<br />
0 0 5 −3<br />
0 0 10 −6<br />
0 0 0 1<br />
<br />
1 1 −1 1<br />
0 0 5 −3<br />
0 0 0 1<br />
0 0 0 0<br />
<br />
1 1 −1 1<br />
<br />
0 0 1 0<br />
0 0 0 1<br />
0 0 0 0<br />
¢