7
} ﻞ ﻗُ ﺎ ﻟ ﱠﻦﻣ ﻭﻰﺑﺮﻘ ﺍﻟﻲ ﻓﺓﺩﻮﻤ ﺍﻟﺎ ﻟ ﺇﺍﺮﺟ ﺃﻪﻴﻠ ﻋﻢﻜ ﻟﺄﺳ ﺃ ُ ْ ِ ْ ﱠِ َ ِ َ ُ ُ َ َ ﻑﺮﺘﻘ ﻳ ِ َ ْ ﻮﺭﻜ ﺷﻮﺭﻔ ﻏﻪ ﺍﻟﻠﻥ ﺇﺎﻨﺴ ﺣﺎﻴﻬ ﻓﻪ ﻟﺩﺰ ﻧﺔﻨﺴ ﺣ ُ ُ َ ﱠ ِ ِ َ ِ ﱠً { } ﻢﻜ ﻟﺄﺳ ﺃ ﻻﻡﻮ ﻗﺎ ﻳ ُ ُ َ َ ِ َ ﻪﻴﻠ ﻋِ َ ﺇﺍﺮﺟ ﺃِ َ ﻼﻓ ﺃﻲ ﻧﺮﻄ ﻓﻱﺬ ﺍﻟﻰﻠ ﻋﻻ ﺇﻱﺮﺟ ﺃ ﻥ َ َ ِ َ َ ِ ﱠَ ﱠِ ِ َ ﻮﻥﻠﻘﻌ ﺗ ُ ِ َ { [email protected] ﺨﻁﻲ ﺠﺒﺭ ﺍﻟﺜﺎﻟﺜﺔ ﺍﻟﻔﺭﻗﺔ– ﺍﻟﺘﺭﺒﻴﺔ ﻜﻠﻴﺔ– ﺍﻟﺭﻴﺎﻀﻴﺎﺕ ﻗﺴﻡ ﺃﻭل ﺘﺭﻡ ﻟﻠﺤﺫﻑ ﺠﺎﻭﺱ ﺒﻁﺭﻴﻘﺔ ﺍﻟﺨﻁﻴﺔ ﺍﻟﻤﻌﺎﺩﻻﺕ ﺤل ﺍﻟﻤﺼﻔﻭﻓﺔ ﺭﺘﺒﺔ ﺘﻌﺭﻴﻑ: ﺍﻟﻤﺼﻔﻭﻓﺔA ﻤﻥ ﻤﻜﻭﻨﺔn ﻭ ﺍﻟﺼﻔﻭﻑ ﻤﻥm ﺍﻟﺘﺎﻟﻴﺔ ﺍﻟﺼﻭﺭﺓ ﻋﻠﻰ ﺍﻷﻋﻤﺩﺓ ﻤﻥ11 12 1 21 22 2 1 2 m m n n nm a a a a a a A a a a = ﻤﺤﺩﺩ ﺃﻜﺒﺭ ﺩﺭﺠﺔ ﻫﻲ ﺍﻟﻤﺼﻔﻭﻓﺔ ﺭﺘﺒﺔ ﻴﺴﺎﻭ ﻻ ﻱ ﺒﺎﻟﺭﻤﺯ ﻟﻬﺎ ﻭﻴﺭﻤﺯ ﺍﻟﺼﻔﺭRank(A) ﻤﺜﺎل: ﺍﻟﻤﺼﻔﻭﻓﺔ ﺭﺘﺒﺔ ﺃﻭﺠﺩ0 1 2 1 1 2 3 2 3 1 1 3 A = ؟ ﺍﻟﺤل: ﺍﻟﻤﺼﻔﻭﻓﺔ ﺇﻥ ﺤﻴﺙA ﻴﻤﻜﻥ ﻤﺤﺩﺩ ﺃﻜﺒﺭ ﻓﺈﻥ ﺃﻋﻤﺩﺓ ﻭﺃﺭﺒﻌﺔ ﺼﻔﻭﻑ ﺜﻼﺜﺔ ﻤﻥ ﻤﻜﻭﻨﺔ ﺍﻟﺜﺎﻟﺜﺔ، ﺍﻟﺩﺭﺠﺔ ﻤﻥ ﻫﻭ ﺘﻜﻭﻴﻨﻪ ﻫﻡ ﺍﻟﺜﺎﻟﺜﺔ ﺍﻟﺩﺭﺠﺔ ﻤﻥ ﻤﺤﻴﺩﺩﺍﺕ ﺃﺭﺒﻊ ﺘﺤﺘﻭﻱ ﺍﻟﻤﺼﻔﻭﻓﺔ ﻫﺫﻩ ﺇﺫﻥ: 0 1 2 1 2 3 2 3 1 1 =- , 0 1 1 1 2 2 2 3 1 3 =- , 0 2 1 1 3 2 2 3 1 3 =- , 1 2 1 2 3 2 2 1 1 3 =- ﺍﻟﻤﺼﻔﻭﻓﺔ ﺭﺘﺒﺔ ﺃﻥ ﻴﻌﻨﻲ ﻭﻫﺫﺍA ﻫﻲ3 ﺃﻭRank(A)=3 ﻭﺍﻵﻥ ﺍﻟﻤﺼﻔﻭﻓﺔ ﺃﻋﻤﺩﺓ ﺃﻭ ﺼﻔﻭﻑ ﻋﻠﻰ ﻨﺠﺭﻱ ﺴﻭﻑA ﺘﺴﻤﻰ ﻭﺍﻟﺘﻲ ﺍﻵﺘﻴﺔ ﺍﻟﺘﻐﻴﻴﺭﺍﺕ ﻤ ﻤﻊ ﺍﻻﺒﺘﺩﺍﺌﻴﺔ، ﺒﺎﻟﺘﻐﻴﻴﺭﺍﺕ ﺃﻭ ﻓﻘﻁ ﺍﻟﺼﻔﻭﻑ ﻋﻠﻰ ﺇﺠﺭﺍﺅﻫﺎ ﻴﺘﻡ ﺇﻤﺎ ﺍﻟﺘﻐﻴﺭﺍﺕ ﻫﺫﻩ ﺃﻥ ﻼﺤﻅﺔ ﻓﻘﻁ ﺍﻷﻋﻤﺩﺓ ﻋﻠﻰ.
Un Gabr 31 Gauss
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-
{ }
moc.oohay@hn_demmahoM { }
:
m n A 1 21 11
2 22 12
2 1
m
m
mn n n
a a aa a a
A
a a a
=
)A(knaR
:
1 2 1 02 3 2 13 1 1 3
A =
A :
: 2 1 02 3 2 11 1 3
, - =1 1 02 2 2 13 1 3
, - =1 2 02 2 3 13 1 3
, - =1 2 12 2 3 23 1 1
- =
3=)A(knaR 3 A
A
.
-
{ }
moc.oohay@hn_demmahoM { }
. :
. ( ) / .1 / ( ) / .2
.( ) . ( ) .3
:
: n m 1 1 2 21 1 11
2 2 2 22 1 12
2 2 1 1
n n
n n
n n nm m m
b x a x a x ab x a x a x a
b x a x a x a
= + + += + + +
= + + +
)1.1(
)1.1( .
=B XA :
1 21 11
2 22 12
2 1
n
n
nm m m
a a aa a a
A
a a a
=
,
1
2
n
xx
X
x
=
,
1
2
n
bb
B
b
=
. B X A B,A
)B|A(
-
{ }
moc.oohay@hn_demmahoM { }
1 1 21 11
2 2 22 12
2 1
) | (
n
n
n nm m m
b a a ab a a a
B A
b a a a
=
3x,2x,1x
.
=)B|A(knar=)A(knar . 1
. )B|A(knar=)A(knar < . 2
. . )A(knar < )B|A(knar . 3
:
1 2 21 1 11
2 2 22 1 12
2 2 1 1
00
0
n n
n n
n nm m m
x a x a x ax a x a x a
x a x a x a
= + + += + + +
= + + +
= XA0 1 21 11
2 22 12
2 1
n
n
nm m m
a a aa a a
A
a a a
=
.
0=nx==2x=1x
-
{ }
moc.oohay@hn_demmahoM { }
: / )A(nar = . 1
. )A(knar < . 2
.
:
.
:
( ) / . 1 (. )
. . 2 . . 3
:
: 3
5 4 2 32 5 3 4
z y xz y xz y x
= + += + -= - +
. :
-
{ }
moc.oohay@hn_demmahoM { }
) (3 1 1 1 3 1 1 1 3 1 1 1
01 9 1 0 ~ 4 1 5 0 ~ 5 4 2 3 |4 1 5 0 01 9 1 0 2 5 3 4
B A - - - = - - - - - -
3 1 1 1 3 1 1 101 9 1 0 ~ 01 9 1 0 ~
1 1 0 0 64 64 0 0
= = =x y z1 ,1 ,1
:
x y
.
:
) 10 (3 3 2
4 8 3 21 71 2 3
z y xz y xz y x
= + += + += + +
) 20 (5 2 3 2
2 3 21 4 4
z y xz y x
z y x
= - += + -
= + -
) 30 (5 3 25 2 2 361 3 5
z y xz y xz y x
= - += + -= - -
-
} {
} { [email protected]
( 04 ) 2 3 3
2 4 4 3 93 6 8 10
x y z wx y z wx y z w
+ - + =+ + + =+ - + =
( 05 ) 2 3 2 2
2 5 8 6 53 4 5 2 4
x y z wx y z wx y z w
+ - + =+ - + =+ - + =
( 06 ) 5 4 13 3
3 2 5 22 2 3 4 1
x y z wx y z wx y z w
+ + - =- + + =+ + - =
( 07 ) 2 5 4 0
2 3 2 3 04 7 6 0
x y z wx y z wx y z w
+ - + =- + + =- + - =
( 08 ) 3 2 0
2 3 03 2 2 0
x y zx y zx y z
+ - =- + =- + =
( 09 )
2 2 02 2 03 4 6 03 11 12 0
x y zx y zx y zx y z
- + =+ - =+ - =- + =
( 10 )
52 3 2
2 2 3 33 2 1
x y z ux y z u
x z ux y u
- - - =+ + + = -
+ + =+ + =
-
{ }
moc.oohay@hn_demmahoM { }
) 11 (
51 2 30 2 3 511 3 33 7 11
z y xz y xz y xy x
- = - += + += + +- = +
) 21 (3 2
3 3 20
w z y xy x
u z y x
= - + -= -
= + - -
) 31 (4 32 2
9 7 3
z y xz y xz y x
= - += + += + +
) 41 (6
3 26 2 3
u z y xz y xu y x
= + + += - += + +
) 51 (0 2 3
0 2 20 2
z y xz y xy x
= + -= + - -= + -
) 61 (0 2
0 20 3
z y xz y xz y x
= + += + += + -
) 71 (0 3
0 6 20 2 3
u z y xu z y xu z y x
= + + -= - - -
= + + + -
/moc.draobtaerg.bam.www//:ptth
