(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

¥£ ¦£¥¡ ¤§ ¦£¡
58 CAPÍTULO 5.
am
= cm
m
= ac
an am an bp bq bp bq
+ + + cn dp dq cm cn dp dq
n m n p q p
+ ad
+ bc
+ bd
q
m n
p q
m n
= ac × 0 + ad (mq − pn) + bc (pn − mq) + bd × 0
p q
= ad (mq − pn) − bc (mq − pn) = (mq − np) (ad − bc)
¢¡¤£ ¦¥¨§¨© ¦ ¡ § ¤¤¥¦ ¡ ¥ 1 2 3
¦¥ ¦§ §
¡ ¨ abc = 0£¢
bc a 2 a 2
b 2 ac b 2
c 2 c 2 ab
a b c
=
¨
¨¥
bc
abc
a2 a2 b2 ac b2 c2 c2
ab
abc
= bc
a2 a2 ab2 ac b2 ac2 c2
abc
= c
ab
ba2 a2 ab2 bac b2 ac2 bc2
ab
=
= a
= ab
= abc
bc
a2 a2 b2 ac b2 c2 c2
ab
=
¡ ¨
A =
d e f
g h i
a b c
bc ba ca
ab 2 bac cb 2
ac 2 bc 2 cab
bc ab ac
ab ac bc
ac bc ab
a b c
d e f
g h i
bc ba ca
ab ac cb
ac 2 bc 2 cab
det A = γ
γ £¢ ©
a + g b + h c + i
d e f
g h i
b e h
a d g
c f i
¨¥ ¨ A =
a b c
d e f
g h i
3a 3b 3c
−d −e −f
4g 4h 4i
bc ab ac
ab ac bc
ac bc ab
abc ba 2 ca 2
ab 2 bac cb 2
ac 2 bc 2 cab
bc ba ca
ab ac cb
ac bc ab
¢ ¢
−3a −3b −3c
d e f
g − 4d h − 4e i − 4f
det A =
γ
¢