(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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40 CAPÍTULO 4. ¦ £§ ¥£ £¡ ¦§©££¢¡ £ §¥£<br />
−−−−→<br />
ℓ3 + ℓ1<br />
<br />
1 1 −1 | 0<br />
0 −1 2 | 1<br />
0 1 −2 | −1<br />
r ([A3 | B3]) = 2<br />
−−−−→<br />
ℓ3 + ℓ2<br />
<br />
1 1 −1 | 0<br />
0 −1 2 | 1<br />
0 0 0 | 0<br />
<br />
= [A ′ 3 | B′ 3 ]<br />
r (A3) = r ([A3 | B3]) = 2 < 3<br />
<br />
¢ ¢ 3 − r (A3) = 1<br />
<br />
(S3) ¡ ¢ <br />
¢ ¢ [A ′ 3 | B′ 3 ]<br />
¢ <br />
<br />
<br />
[A ′ 3 | B′ 3 ] =<br />
−−−−→<br />
ℓ1 − ℓ2<br />
<br />
1 1 −1 | 0<br />
0 −1 2 | 1<br />
0 0 0 | 0<br />
<br />
1 0 1 | 1<br />
0 1 −2 | −1<br />
0 0 0 | 0<br />
<br />
1 1 −1 | 0<br />
−−−−→<br />
−ℓ2 0 1 −2 | −1<br />
0 0 0 | 0<br />
<br />
= [A3” | B3”]<br />
¥ B3” <br />
A3”X =<br />
<br />
1 0 1<br />
<br />
x<br />
<br />
1<br />
<br />
0 1 −2<br />
0 0 0<br />
y<br />
z<br />
=<br />
(S3)<br />
−1<br />
0<br />
⇐⇒<br />
⇐⇒<br />
<br />
x + z<br />
y − 2z<br />
0<br />
<br />
x<br />
y<br />
z<br />
<br />
=<br />
<br />
=<br />
1<br />
−1<br />
0<br />
1 − z<br />
−1 + 2z<br />
z<br />
<br />
[1 − z, −1 + 2z, z]<br />
¡ T | z ∈ <br />
IR<br />
¡ (S4) £¢ ¢ ©<br />
(S4)<br />
⎧<br />
⎨<br />
⎩<br />
x + 2y = 1<br />
x + y = 1<br />
−x + y = −1<br />
⇐⇒<br />
2<br />
4<br />
1 2 0<br />
1 1 0<br />
−1 1 0<br />
| {z }<br />
A4<br />
⇐⇒ A4X = B4<br />
3 2<br />
5 4 x<br />
y<br />
z<br />
3<br />
5<br />
| {z }<br />
X<br />
=<br />
<br />
<br />
2<br />
4<br />
1<br />
1<br />
3<br />
5<br />
−1<br />
| {z }<br />
¢ A4 ¢ ¢ <br />
<br />
¢<br />
<br />
A4 =<br />
−−−−−→<br />
ℓ3 + 3ℓ2<br />
<br />
1 2 0<br />
1 1 0<br />
−1 1 0<br />
<br />
1 2 0<br />
0 −1 0<br />
0 0 0<br />
−−−−→<br />
ℓ2 − ℓ1<br />
<br />
1 2 0<br />
0 −1 0<br />
−1 1 0<br />
−−−−→<br />
ℓ3 + ℓ1<br />
B4<br />
1 2 0<br />
0 −1 0<br />
0 3 0