(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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44 CAPÍTULO 4. ¦ £§ ¥£ £¡ ¦§©££¢¡ £ §¥£<br />
−−−−−→<br />
ℓ2 − 1<br />
2 ℓ1<br />
⎡<br />
⎢<br />
⎣<br />
2 −1 1 | −1<br />
0<br />
5<br />
2<br />
1<br />
2 |<br />
1<br />
2<br />
0 − 5<br />
2<br />
1<br />
− 2 | − 1<br />
2<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
r ([A7 | B7]) = 2 <br />
3 − r (A7) = 1<br />
⎤<br />
⎥<br />
⎦ −−−−→<br />
ℓ3 + ℓ2<br />
⎡<br />
⎢<br />
⎣<br />
2 −1 1 | −1<br />
0<br />
5<br />
2<br />
1<br />
2 |<br />
1<br />
2<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
⎤<br />
⎥<br />
⎦ = [A′ 7 | B ′ 7]<br />
r (A7) = r ([A7 | B7]) = 2 <br />
(S7) ¡ ¢ ¢<br />
¢ <br />
<br />
<br />
¢ ¢ [A ′ 7 | B′ 7 ]<br />
¢ <br />
<br />
[A ′ 7 | B ′ 7] =<br />
−−−−→<br />
ℓ1 + ℓ2<br />
⎡<br />
⎢<br />
⎣<br />
⎡<br />
⎢<br />
⎣<br />
2 −1 1 | −1<br />
0<br />
5<br />
2<br />
1<br />
2 |<br />
1<br />
2<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
2 0<br />
0 1<br />
6<br />
| − 5 4<br />
5<br />
1<br />
1<br />
| 5<br />
5<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
⎤<br />
⎡<br />
⎥<br />
⎦ −−−−→<br />
2<br />
5 ℓ2<br />
⎢<br />
⎣<br />
⎤<br />
⎥<br />
⎦ = [A7” | B7”]<br />
A7”X = B7” <br />
¥<br />
⎡<br />
⎡<br />
⎢<br />
⎣<br />
2<br />
0<br />
0<br />
1<br />
6<br />
5<br />
1<br />
5<br />
0 0 0<br />
0 0 0<br />
0 0 0<br />
⎤<br />
⎥<br />
⎦<br />
x<br />
y<br />
z<br />
<br />
⎢<br />
= ⎣<br />
− 4<br />
5<br />
1<br />
5<br />
0<br />
0<br />
0<br />
⎤<br />
⎥<br />
⎦ ⇐⇒<br />
⇐⇒<br />
2 −1 1 | −1<br />
0 1<br />
1<br />
5 |<br />
1<br />
5<br />
0 0 0 | 0<br />
2x + 6<br />
5 z<br />
y + 1<br />
5 z<br />
x<br />
y<br />
0 0 0 | 0<br />
0 0 0 | 0<br />
<br />
=<br />
1<br />
−<br />
5 =<br />
1<br />
5<br />
− 4<br />
5<br />
1<br />
5<br />
(3z + 2)<br />
(1 − z)<br />
(S7) ¡ 1<br />
1<br />
− (3z + 2) , 5 5 (1 − z) , z T<br />
| z <br />
∈ IR<br />
¡ (S8) £¢ ¢ ©<br />
(S8)<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
−5x − 2y + z = −1<br />
6x + 2y + z = 0<br />
−4x − 2y + 3z = −2<br />
2x + 4z = −2<br />
−6x − 3y + 2z = −1<br />
⇐⇒<br />
2<br />
3<br />
−5 −2 1<br />
6 6 2 1 7 2<br />
6<br />
7<br />
6 −4 −2 3 7 4<br />
6<br />
7<br />
4 2 0 4 5<br />
−6 −3 2<br />
| {z }<br />
x<br />
3<br />
y 5<br />
z<br />
| {z }<br />
X<br />
A8<br />
⇐⇒ A8X = B8<br />
=<br />
⎤<br />
⎥<br />
⎦<br />
<br />
<br />
2<br />
−1<br />
3<br />
6<br />
4<br />
0<br />
−2<br />
−2<br />
7<br />
5<br />
−1<br />
| {z }<br />
B8