(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
100 CAPÍTULO 9. £¡ §© ¢¦£ ¤ ¢¥ § ¡<br />
<br />
1 1 ¢ 0 0 <br />
<br />
§ ¢ ¡ <br />
<br />
<br />
0 0 1 1<br />
((1, 1, 0, 0), (0, 0, 1, 0)) F<br />
(a, b, c, d) ∈ G<br />
<br />
£¢<br />
<br />
b − c = 0<br />
d = 0<br />
⇐⇒<br />
G ¢ <br />
<br />
G = {(a, b, b, 0) | a, b ∈ IR}<br />
1 0 0 0<br />
2<br />
b = c<br />
d = 0<br />
= {a(1, 0, 0, 0) + b(0, 1, 1, 0) | a, b ∈ IR}<br />
= 〈(1, 0, 0, 0), (0, 1, 1, 0)〉<br />
0 1 1 1<br />
¢ <br />
<br />
§ ¢ ((1, 0, 0, 0), (0, 1, 1, 0)) ¡ G dim G =<br />
<br />
<br />
¡<br />
<br />
(a, b, c, d) ∈ F ∩ G <br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
( a − b = 0<br />
a = b + d<br />
( b − c = 0<br />
£¢ (a, b, c, d) ∈ F (a, b, c, d) ∈ G<br />
d = 0<br />
⇐⇒<br />
a = b<br />
d = 0<br />
b = c<br />
F ∩ G ¢ <br />
<br />
F ∩ G = {(a, a, a, 0) | a, c ∈ IR}<br />
<br />
[ 1 1 1 0 ]<br />
= {a(1, 1, 1, 0) | a ∈ IR}<br />
= 〈(1, 1, 1, 0)〉<br />
<br />
<br />
§ ¢<br />
¢ <br />
((1, 1, 1, 0)) ¡ <br />
¢ ¢ <br />
F ∩ G<br />
<br />
1 0 0 3<br />
2 0 0 1<br />
<br />
<br />
<br />
1 0 0 3<br />
2 0 0 1<br />
−−−−−→<br />
ℓ2 − 2ℓ1<br />
−−−−−→<br />
ℓ1 − 3ℓ2<br />
<br />
1 0 0 3<br />
0 0 0 −5<br />
<br />
1 0 0 0<br />
0 0 0 1<br />
<br />
−−−−→<br />
− 1<br />
5 ℓ2<br />
1 0 0 3<br />
0 0 0 1