(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

38 CAPÍTULO 4. ¦ £§ ¥£ £¡ ¦§©££¢¡ £ §¥£
A1 =
1 1 2
2 −1 1
0 3 3
−−−−−→
ℓ2 − 2ℓ1
1 1 2
0 −3 −3
0 3 3
−−−−→
ℓ3 + ℓ2
1 1 2
0 −3 −3
0 0 0
r (A1) = 2
¢
¡
A1
¢
[A1 | B1] =
−−−−→
ℓ3 + ℓ2
1 1 2 | 1
2 −1 1 | 1
0 3 3 | 0
1 1 2 | 1
0 −3 −3 | −1
0 0 0 | −1
−−−−−→
ℓ2 − 2ℓ1
1 1 2 | 1
0 −3 −3 | −1
0 3 3 | 0
r ([A1 | B1]) = 3
r (A1) < r ([A1 | B1])
(S1) ¡
§ (S2) £¢ ¢ ©
(S2)
⎧
⎨
⎩
x + y − z = 0
2x + y = 1
x − z = 1
⇐⇒
2
4
1
2
1
1
−1
0
1 0 −1
| {z }
A2
⇐⇒ A2X = B2
3 2
5 4 x
y
z
3
5
| {z }
X
=
2
4 0
1
3
5
1
| {z }
¢ A2 ¢ ¢
¢
A2 =
−−−−→
ℓ3 − ℓ2
1 1 −1
2 1 0
1 0 −1
1 1 −1
0 −1 2
0 0 −2
−−−−−→
ℓ2 − 2ℓ1
1 1 −1
0 −1 2
1 0 −1
−−−−→
ℓ3 − ℓ1
B2
1 1 −1
0 −1 2
0 −1 0
r (A2) = 3
¢
¡
A2
¢
[A2 | B2] =
−−−−→
ℓ3 − ℓ1
1 1 −1 | 0
2 1 0 | 1
1 0 −1 | 1
1 1 −1 | 0
0 −1 2 | 1
0 −1 0 | 1
−−−−−→
ℓ2 − 2ℓ1
−−−−→
ℓ3 − ℓ2
1 1 −1 | 0
0 −1 2 | 1
1 0 −1 | 1
1 1 −1 | 0
0 −1 2 | 1
0 0 −2 | 0
= [A ′ 2 | B ′ 2]