(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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198 CAPÍTULO 15. ¦£¦£ ££<br />
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−2 2 3<br />
1 −1 0<br />
− 2<br />
3<br />
2<br />
3 0<br />
−−−−−→<br />
ℓ1 ↔ ℓ2<br />
<br />
1 −1 0<br />
−2 2 3<br />
− 2<br />
<br />
3<br />
1<br />
2<br />
3<br />
−1<br />
0<br />
0<br />
−2 2 3<br />
0 0 0<br />
−−−→<br />
3ℓ3<br />
1 −1 0<br />
−2 2 3<br />
−2 2 0<br />
¤ (A − 3I3)X = 0 ©<br />
<br />
<br />
M3 =<br />
−−−−−→<br />
ℓ3 + 2ℓ1<br />
=<br />
=<br />
M3 <br />
<br />
<br />
¢<br />
<br />
a<br />
b<br />
c<br />
<br />
a<br />
b<br />
c<br />
b<br />
=<br />
b<br />
0<br />
<br />
<br />
<br />
(1) + ¢<br />
1<br />
<br />
1 −1 0<br />
−−−−−→<br />
ℓ2 + 2ℓ1 0 0 3<br />
0 0 0<br />
∈ M3×1(IR) | a − b <br />
= 0 c = 0<br />
∈ M3×1(IR) | a <br />
= b c = 0<br />
| b ∈ IR<br />
1<br />
0<br />
<br />
=<br />
1<br />
¢<br />
(2) + ¢<br />
1<br />
0<br />
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<br />
¢<br />
§ £ ¡ ¢ ¨ ¥ § ¢ ¡<br />
<br />
−−−−→<br />
1<br />
3 ℓ2<br />
<br />
1 −1 0<br />
0 0 1<br />
0 0 0<br />
(3) = dim M3 = 1<br />
(3) = 1 + 1 + 1 = 3<br />
<br />
A<br />
¡ ¢ ¨ £¢ ¤ <br />
<br />
P M3×3(IR) ¨ <br />
∈<br />
¤<br />
P −1 AP =<br />
<br />
α1 0 0<br />
0 α2 0<br />
0 0 α3<br />
<br />
=<br />
1 0 0<br />
0 2 0<br />
0 0 3<br />
P ¡ −1 0 <br />
1<br />
<br />
1 1 1<br />
− 2<br />
3<br />
2<br />
− 3 0
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