(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

36 CAPÍTULO 4. ¦ £§ ¥£ £¡ ¦§©££¢¡ £ §¥£
[1, 0, 1, 0] T ¢¢¡ ¢ ¢
¢ A £¢ ¢
¢
A =
−−−−→
ℓ3 + ℓ2
1 1 2 −1
2 2 −2 2
0 0 6 −4
1 1 2 −1
0 0 −6 4
0 0 0 0
−−−−−→
ℓ2 − 2ℓ1
1 1 2 −1
0 0 −6 4
0 0 6 −4
A
¡
r (A) = 2
¢
¢
[A | B] =
−−−−→
ℓ3 + ℓ2
1 1 2 −1 | −1
2 2 −2 2 | 4
0 0 6 −4 | −6
1 1 2 −1 | −1
0 0 −6 4 | 6
0 0 0 0 | 0
−−−−−→
ℓ2 − 2ℓ1
= [A ′ | B ′ ]
1 1 2 −1 | −1
0 0 −6 4 | 6
0 0 6 −4 | −6
r ([A | B]) = 2 r (A) = r ([A | B]) = 2 < 4
¡ ¢ ¢ ¢
(S)
¢ ¢ [A ′ | B ′ ¢
]
4 − r (A) = 2
[A ′ | B ′ ] =
−−−→
− 1
6 ℓ2
1 1 2 −1 | −1
0 0 −6 4 | 6
0 0 0 0 | 0
1 1 0
1
3 | 1
0 0 1 − 2
0 0 0
3
0
|
|
−1
0
−−−−−→
ℓ1 + 1
3 ℓ2
= [A” | B”]
¥ B”
A”X =
1 1 0
1 x
3
0 0 1 − 2
3
0 0 0 0
y
z
w
1
=
−1
0
⇐⇒
⇐⇒
1 1 0
1
3 | 1
0 0 −6 4 | 6
0 0 0 0 | 0
w
x + y + = 1 3
z − 2
w = −1
3
x = 1 − y − w
3
z = −1 + 2
3 w
1 w
2
− y − , y, −1 + 3 3w, w
T
| (y, w) ∈ IR
(S) ¡