Free Essay

Obada

In: Social Issues

Submitted By obada
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 1
‫/ 1102 م‬

/

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

  :[1-3]


 1


 

 
..................................................................................................................

،،، 


27

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


2012/2011
‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫اﻟﺤﺎدي‬

2012/2011

‫1 ‪‬‬

‫]3-1[: ‪ ‬‬

‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫‪‬‬
‫ﻋﻨﺪ ﺿﺮﺏ ﻣﺼﻔﻮﻓﺔ ﰲ ﻋﺪﺩ ﻳﺴﻤﻰ ﺑﺎﻟﻌﺪﺩ ﺍﻟﻘﻴﺎﺳﻲ ﻓﺈﻧﻨﺎ ﻧﻀﺮﺏ ﻛﻞ ﻋﻨﺼﺮ ﻣﻦ ﺍﳌﺼﻔﻮﻓﺔ ﰲ ﻫﺬﺍ ﺍﻟﻌﺪﺩ ﻭﺗﻜﻮﻥ‬
‫ﺭﺗﺒﺔ ﺍﳌﺼﻔﻮﻓﺔ ﺍﻟﻨﺎﲡﺔ ﻧﻔﺲ ﺭﺗﺒﺔ ﺍﳌﺼﻔﻮﻓﺔ ﺍﻷﺻﻠﻴﺔ .‬

‫ﺇﺫﺍ ﻛﺎﻥ ﺍﳌﺼﻔﻮﻓﺔ ‪ A‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ ‪ ، m n‬ﻭﺍﳌﺼﻔﻮﻓﺔ ‪ B‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ ‪ n  p‬ﻓﺈﻥ ﺣﺎﺻﻞ ﺿﺮﺏ ‪ AB‬ﻳﻜﻮﻥ‬
‫ﻣﻌﺮﻑ ﺇﺫﺍ ﻭﻓﻘﻂ ﺇﺫﺍ ﻛﺎﻥ ﻋﺪﺩ ﺍﻷﻋﻤﺪﺓ ﰲ ﺍﳌﺼﻔﻮﻓﺔ ‪ A‬ﻳﺴﺎﻭﻱ ﻋﺪﺩ ﺍﻟﺼﻔﻮﻑ ﰲ ﺍﳌﺼﻔﻮﻓﺔ ‪ B‬ﻭﺗﻜﻮﻥ ﺭﺗﺒﺔ‬

‫ﺃﻱ ﺃﻥ : ‪A m×n × B n×p = C m×p‬‬

‫ﺍﳌﺼﻔﻮﻓﺔ ﺍﻟﻨﺎﲡﺔ ﻣﻦ ﺍﻟﻀﺮﺏ ‪ C‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ ‪m  p‬‬

‫اﻟﺤﺎدي‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪0 1 4‬‬
‫‪3 2 1 ‬‬
‫‪‬‬
‫‪‬‬

‫‪ 3 −1‬‬
‫= ‪7 −3 , C‬‬
‫‪‬‬
‫‪‬‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫‪1 −2 0 ‬‬
‫‪A=‬‬
‫=‪, B‬‬
‫‪6 4 2‬‬
‫‪‬‬
‫‪‬‬

‫...................................................................................................................................................................................‬

‫= ‪A× B‬‬

‫)1(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪B×C‬‬

‫)2(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫...................................................................................................................................................................................‬

‫= ‪A×C‬‬

‫‪ 1‬‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪1 −1 5 ‬‬
‫‪2 3 4‬‬
‫‪‬‬
‫‪‬‬

‫‪ 5 0‬‬
‫= ‪ −3 1  , C‬‬
‫‪‬‬
‫‪‬‬

‫‪ 2 0‬‬
‫‪A=‬‬
‫=‪ , B‬‬
‫‪ −1 3‬‬
‫)3(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪A× B‬‬

‫)4(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

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  :[1-3]

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

2012/2011

3
A = 1

6

(1)

5
 −2
− 3 ; B =  5


 2
− 4



1
2
0 ; C =

0
− 6


6
1


: ‫ﺃﻭﻻﹰ ﺿﺮﺏ ﻋﺪﺩ ﰲ ﻣﺼﻔﻮﻓﺔ‬
: ‫ﺃﻭﺟـــﺪ ﺃﻥ ﺃﻣﻜﻦ‬

2A=

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

(2)

3B=

...................................................................................................................................................................................................................................................

(3)

‫اﻟﺤﺎدي‬

...................................................................................................................................................................................................................................................

2
C=
3

...................................................................................................................................................................................................................................................

(4)

2A + B=

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

(5)

A + 3B =

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

 1

5 0
3 A =  −1 −2  , B =


3 −3 


(5)

C× B =

(6)

C2 =

 1 2
 −3 0  , C =


 −1 4 



 2 −3 
1 −2 



: ‫ﺇﺫﺍ ﻛﺎﻧﺖ‬

: ‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ‬

..................................................................................................................................

...................................................................................................................................................................................

..........................................................................................................................................................................................................................................
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29

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

...................................................................................................................................................................................................................................................

 1
‫/ 1102 م‬

/

  :[1-3]

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

2012/2011


: ‫ﺣــﻞ ﻛﻼﹰ ﻣﻦ ﺍﳌﻌﺎﺩﻻﺕ ﺍﳌﺼﻔﻮﻓﻴــﺔ ﺍﻟﺘﺎﻟﻴـــﺔ‬

(6)

1 − 1  −2 8
4x + 
=
 + 3x
 2 0  6 − 4 

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

...................................................................................................................................................................................................................................................

(7)

3 − 3  −3 9
2x + 
=
−x
4 0  5 − 6 

 


...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

 1

...................................................................................................................................................................................................................................................

(8)

3 − 3  −3 9 
2
x+
=
4 0  5 − 6 
3

 


...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
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30

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

...................................................................................................................................................................................................................................................

‫اﻟﺤﺎدي‬

...................................................................................................................................................................................................................................................

 1
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/

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

  :[1-3]
2012/2011

(9)

1 − 5 −2
4x − 
=
6 2   −4

 

: ‫ﺣــﻞ ﻛﻼﹰ ﻣﻦ ﺍﳌﻌﺎﺩﻻﺕ ﺍﳌﺼﻔﻮﻓﻴــﺔ ﺍﻟﺘﺎﻟﻴـــﺔ‬

11 
− 6


...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

(7)

3 −1
1 7 
2X + 
= 


0 5 
4 1

...................................................................................................................................................................................................................................................

‫اﻟﺤﺎدي‬

...................................................................................................................................................................................................................................................

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

(8)

 −1
 −3
2X +   =   − X
4
 7

..........................................................................................................................................................................................................................................
..........................................................................................................................................................................................................................................

 1

..........................................................................................................................................................................................................................................
..........................................................................................................................................................................................................................................
..........................................................................................................................................................................................................................................

(9)

3 −1
 −2 5 
= 
− X
2X + 
4 0
7 −4 





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31

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

...................................................................................................................................................................................................................................................

‫]3-1[: ‪ ‬‬

‫1 ‪‬‬
‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫ﺣــﻞ ﻛﻼﹰ ﻣﻦ ﺍﳌﻌﺎﺩﻻﺕ ﺍﳌﺼﻔﻮﻓﻴــﺔ ﺍﻟﺘﺎﻟﻴـــﺔ :‬

‫‪ −2 5 −4‬‬
‫‪0 1 2 ‬‬
‫‪= ‬‬
‫‪‬‬
‫‪−1 −6‬‬
‫‪‬‬
‫‪1 3 5 ‬‬

‫‪(10) 2X + ‬‬
‫3‪‬‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫اﻣﺘﺤﺎن ﻋﺠﻤﺎن 9002 / 0102 م‬

‫اﻟﺤﺎدي‬

‫)11( ﺣﻞ ﺍﳌﻌﺎﺩﻟﺔ ﺍﳌﺼﻔﻮﻓﻴﺔ ﺍﻟﺘﺎﻟﻴﺔ :‬

‫‪ 4 2 −3‬‬
‫‪ −1 7 7 ‬‬
‫‪= ‬‬
‫‪− 5x‬‬
‫‪1 0 7 ‬‬
‫1‬
‫‪2 −8‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
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‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 6002 / 7002 م‬

‫‪ −2 5 ‬‬
‫‪ 2 −1‬‬
‫‪2x + ‬‬
‫‪= ‬‬
‫‪‬‬
‫‪‬‬
‫‪ 3 −1‬‬
‫‪ −5 1 ‬‬

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‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫23‬

‫‪ 1‬‬

‫)21( ﺣﻞ ﺍﳌﻌﺎﺩﻟﺔ ﺍﻟﺘﺎﻟﻴﺔ ﻓـﻲ‬

‫‪x‬‬

‫]3-1[: ‪ ‬‬

‫1 ‪‬‬
‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 8002 / 9002 م‬

‫ﺣﻞ ﻛﻼﹰ ﻣﻦ ﺍﳌﻌﺎﺩﻟﺘﲔ ﺍﻟﺘﺎﻟﻴﺘﲔ :‬
‫‪ 3 −1 1 7 ‬‬
‫‪2x + ‬‬
‫‪=‬‬
‫‪‬‬
‫‪0 5   4 1 ‬‬

‫)31(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 7002 / 8002 م‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫ﺣﻞ ﺍﳌﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ :‬

‫‪ 3   −2 ‬‬
‫‪3x +   =   + x‬‬
‫‪ 4  7 ‬‬

‫)41(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫)01(‬

‫ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛﻼﹰ ﻣﻦ ‪ x , y , z‬ﺇﺫﺍ ﻛﺎﻥ :‬

‫‪ 1‬‬

‫اﻣﺘﺤﺎن أم اﻟﻘﯿﻮﯾﻦ 9002 / 0102 م‬

‫‪ 2 x  4 y ‬‬
‫‪ x 9‬‬
‫‪+ ‬‬
‫‪= ‬‬
‫‪y 7‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬
‫‪  −3 2 ‬‬
‫‪ z 9‬‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫33‬

‫]3-1[: ‪ ‬‬

‫1 ‪‬‬
‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 6002 / 7002 م‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪5‬‬
‫‪4‬‬
‫‪‬‬

‫‪− 1‬‬
‫1− ‪‬‬
‫‪; C=‬‬
‫‪2‬‬
‫‪‬‬
‫2 ‪‬‬

‫ﺃﻭﺟﺪ ﻧﺎﺗﺞ ﻛﻞ ﳑﺎ ﻳﻠﻲ ﺇﻥ ﺃﻣﻜﻦ:‬

‫‪− 2‬‬
‫3‪‬‬
‫‪5 ; B = ‬‬
‫‪‬‬
‫1‪‬‬
‫‪0‬‬
‫‪‬‬

‫3 ‪‬‬
‫1 ‪A=‬‬
‫‪‬‬
‫1− ‪‬‬
‫‪‬‬

‫= 21 ‪a 22 × b 21 × c‬‬

‫)11(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫= ‪A× B‬‬

‫)21(‬

‫...................................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫...................................................................................................................................................................................................................................................‬

‫= ‪B×C‬‬

‫)31(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫= ‪B× A‬‬

‫)41(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫ﺍﻟﺸﺮﻁ ﺍﻟﻼﺯﻡ ﻟﻀﺮﺏ ﻣﺼﻔﻮﻓﺔ ﰲ ﻧﻔﺴﻬﺎ ﻫﻮ‬

‫.........................................‬

‫..............................................................................................................................................................................................‬
‫.....................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫43‬

‫‪ 1‬‬

‫=‬

‫2‬

‫‪B‬‬

‫)51(‬

‫1 ‪‬‬

‫]3-1[: ‪ ‬‬

‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫/‬

‫.............................‬

‫/ 1102 م‬

‫1102/2102‬

‫اﻣﺘﺤﺎن دﺑـــﻲ 9002 / 0102 م‬

‫‪0 5‬‬
‫‪3 1‬‬
‫‪‬‬
‫‪‬‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪ −8 5 −1‬‬
‫= ‪0 9 7  , C‬‬
‫‪‬‬
‫‪‬‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫‪ 2 −1‬‬
‫‪A=‬‬
‫=‪, B‬‬
‫‪1 6‬‬
‫‪‬‬
‫‪‬‬
‫= 21 ‪(16) a 21 + b 23 + c‬‬

‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪(17) 2 A + B‬‬

‫..........................................................................................................................................................................................................................................‬

‫=‬

‫...................................................................................................................................................................................‬

‫2‬

‫‪(18) C‬‬

‫..........................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫..........................................................................................................................................................................................................................................‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫= ‪(19) C − A‬‬

‫...................................................................................................................................................................................‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫اﻣﺘﺤﺎن أم اﻟﻘﯿﻮﯾﻦ 9002 / 0102 م‬

‫ﺇﺫﺍ ﻛﺎﻥ :‬

‫‪ 2 3‬‬
‫‪ −1 5‬‬
‫‪‬‬
‫‪‬‬

‫‪ 2 −1 −1‬‬
‫= ‪ 2 0 −3 , C‬‬
‫‪‬‬
‫‪‬‬

‫ﻓﺈﻭﺟـــﺪ ﻣﺎﻳﻠﻲ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻣﻊ ﺑﻴﺎﻥ ﺍﻟﺴﺒﺐ ﺇﺫﺍ ﱂ ﳝﻜﻦ :‬

‫‪1 0‬‬
‫‪A=‬‬
‫=‪ , B‬‬
‫‪ 2 6‬‬

‫...................................................................................................................................................................................‬

‫= ‪(20) 2A − C‬‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫‪ 1‬‬

‫...................................................................................................................................................................................‬

‫= 2‪A‬‬

‫)12(‬

‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪BC‬‬

‫)22(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫=‬

‫2‬

‫‪B‬‬

‫)32(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫53‬

‫]3-1[: ‪ ‬‬

‫1 ‪‬‬
‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 7002 / 8002 م‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪2 3‬‬
‫‪‬‬

‫‪− 3‬‬
‫1−‪, C = ‬‬
‫‪‬‬
‫‪2‬‬
‫‪‬‬

‫‪1‬‬
‫0‪‬‬
‫‪, B=‬‬
‫‪1‬‬
‫‪‬‬
‫4‪‬‬

‫3‪‬‬
‫‪A=‬‬
‫2− ‪‬‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫= 11‪b21 − 3 c‬‬

‫+ 22‪a‬‬

‫)42(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫= ‪2A − B‬‬

‫)52(‬

‫..........................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫..........................................................................................................................................................................................................................................‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫..........................................................................................................................................................................................................................................‬

‫=‪A B‬‬

‫)62(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫=‪AC‬‬

‫)72(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫= 2‪B‬‬

‫)82(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫63‬

‫‪ 1‬‬

‫...................................................................................................................................................................................................................................................‬

‫1 ‪‬‬

‫]3-1[: ‪ ‬‬

‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫اﻣﺘﺤﺎن ﻋﺠﻤﺎن 9002 / 0102 م‬

‫)ﺃﻭﻻﹰ( : ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪ 3 2‬‬
‫‪ −2 1 ‬‬
‫‪‬‬
‫‪‬‬
‫‪0‬‬
‫5‪‬‬
‫‪‬‬
‫‪‬‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫‪ 5 2‬‬
‫= ‪ −3 1  , C‬‬
‫‪‬‬
‫‪‬‬

‫‪ −3 1 ‬‬
‫= ‪A =  2 4 , B‬‬
‫‪‬‬
‫‪‬‬
‫‪ 1 0‬‬
‫‪‬‬
‫‪‬‬
‫= 22 ‪a 23 + b 21 × c‬‬

‫)92(‬

‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪− A‬‬

‫)03(‬

‫..........................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫..........................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................‬

‫= ‪A×B‬‬

‫)13(‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫اﻣﺘﺤﺎن اﻟﺸﺎرﻗﺔ 6002 / 7002 م‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ :‬

‫‪ 3 −2 ‬‬
‫‪3 −1‬‬
‫‪ −1 5 ‬‬
‫‪5  , B=‬‬
‫1‪A = ‬‬
‫‪, C=‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬
‫‪1 2 ‬‬
‫‪ 2 4‬‬
‫‪ −1 0 ‬‬
‫‪‬‬
‫‪‬‬

‫ﻓﺈﻭﺟـــﺪ ) ﺇﻥ ﺃﻣﻜﻦ ( ﻛﻼ ﳑﺎ ﻳﻠﻲ :‬

‫= 21 ‪a 22 + b 21 + c‬‬

‫)23(‬

‫..........................................................................................................................................................................................................................................‬

‫‪ 1‬‬

‫= ‪A×B‬‬

‫)33(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫= ‪2C + B‬‬

‫)43(‬

‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬
‫..........................................................................................................................................................................................................................................‬

‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫73‬

‫]3-1[: ‪ ‬‬

‫1 ‪‬‬
‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ :‪‬‬

‫.............................‬

‫/‬

‫/ 1102 م‬

‫1102/2102‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ‬
‫ﺃﻭﺟﺪ ﻣﺎ ﻳﻠﻲ :‬

‫‪3‬‬
‫‪2‬‬
‫‪1‬‬
‫1‪‬‬
‫1‪‬‬
‫2‪‬‬
‫‪A=‬‬
‫‪, B=‬‬
‫‪, C=‬‬
‫‪‬‬
‫‪‬‬
‫‪‬‬
‫‪ −3 5 ‬‬
‫‪0 − 1 ‬‬
‫‪3 − 2 ‬‬
‫‪(A.B).C‬‬

‫)53(‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫اﻟﺤﺎدي‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

‫...................................................................................................................................................................................................................................................‬

‫)‪(36) A.(B.C‬‬

‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬
‫...................................................................................................................................................................................................................................................‬

‫...................................................................................................................................................................................................................................................‬

‫ﳑﺎ ﺳﺒﻖ ﻧﺴﺘﻨﺘﺞ ﺃﻥ ﻋﻤﻠﻴﺔ ﺿﺮﺏ ﺍﳌﺼﻔﻮﻓﺎﺕ ﻋﻤﻠﻴﺔ‬
‫ﺃﻛﻤﻞ ﻣﺎ ﻳﻠﻲ :‬

‫)73( ﳝﻜﻦ ﺇﳚﺎﺩ 2 ‪A‬‬

‫ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﳌﺼﻔﻮﻓﺔ‬

‫‪A‬‬

‫..................................................‬

‫......................‬

‫)83( ﺇﺫﺍﻛﺎﻧﺖ ‪ A‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ ‪ B ، m × n‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ ‪ n × q‬ﻓﺈﻥ ‪ AB‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ‬

‫.....................‬

‫)93( ﺇﺫﺍﻛﺎﻧﺖ ‪ A‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ 4 × 1 ، ‪ C‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ 2 × 1 ﻭﻛﺎﻥ ‪ AB = C‬ﻓﺈﻥ ‪ B‬ﻣﻦ ﺍﻟﺮﺗﺒﺔ‬
‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‪ ‬ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬

‫‪www.jwaher1.com‬‬

‫............‬

‫83‬

‫‪ 1‬‬

‫...................................................................................................................................................................................................................................................‬

 1
‫/ 1102 م‬

/

  :[1-3]

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

2012/2011

..........................

‫ ﻣﻦ ﺍﻟﺮﺗﺒﺔ‬x . y ‫ﻓﺈﻥ‬
3
A=
2

1  x =   ; y = −1

 3
5
3
; B=
− 1

4

0  ‫ﺍﺫﺍ ﻛﺎﻧﺖ‬


− 1
 3
; C= 
2

1 

(40)

: ‫ﺇﺫﺍ ﻛﺎﻧﺖ‬

: ‫ﻓﺄﻭﺟﺪ ﻛﻼﹰ ﳑﺎ ﺇﻥ ﺃﻣﻜﻦ‬
(41)

B× C=

...................................................................................................................................................................................................................................................

...................................................................................................................................................................................................................................................

‫اﻟﺤﺎدي‬

...................................................................................................................................................................................................................................................

(42)

C × B=

...................................................................................................................................................................................................................................................

(43)

B2 =

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

 1

...................................................................................................................................................................................................................................................

(44)

0
1

2 −1

2
− 5

 × 0
6
0


4
10
1

− 2
4

− 7


...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

39

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

...................................................................................................................................................................................................................................................

 1
‫/ 1102 م‬

/

  :[1-3]

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

.............................

2012/2011

(45)

 −2
2x + 
3

5
−1

: ‫ﺣﻞ ﺍﳌﻌﺎﺩﻟﺔ ﺍﳌﺼﻔﻮﻓﻴﺔ ﺍﻟﺘﺎﻟﻴﺔ‬

− 4
0
= 
− 6

1

2
5


1
3

...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

0
2


− 1  x
0   −3


3
 3
= 
2y 

 −4

− 6
6


...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

 1

..................................................................................................................................................................................................................................................

(47)

x
1


− 2  3
0  1


− 1
4
=  y 
3

− 14
−1 


...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

40

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

(46)

: x , y ‫ﺍﺳﺘﺨﺪﻡ ﺿﺮﺏ ﺍﳌﺼﻔﻮﻓﺎﺕ ﻭﺗﺴﺎﻭﻱ ﺍﳌﺼﻔﻮﻓﺎﺕ ﻹﳚﺎﺩ‬

‫اﻟﺤﺎدي‬

...................................................................................................................................................................................................................................................

 1
‫/ 1102 م‬

  :[1-3]

: ‫ﺍﻟﻴﻮﻡ ﻭﺍﻟﺘﺎﺭﻳﺦ‬

/

.............................

2012/2011

A

2

=4A

: ‫ﻓﺈﺛﺒﺖ ﺃﻥ‬

1 1
A=
 : ‫ﺇﺫﺍ ﻛﺎﻧﺖ‬
 3 3

(48)

...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

 −4 5
: ‫ﺇﺫﺍ ﻛﺎﻧﺖ‬
, C= 
0 3



(49)

: ‫ﻓﺄﻭﺟﺪ ﺇﻥ ﺃﻣﻜﻦ‬

(50) A × B =

...................................................................................................................................................................................................................................................
..................................................................................................................................................................................................................................................

(51) A × C =
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

(52) A

2

=

...................................................................................................................................................................................................................................................

 1

...................................................................................................................................................................................................................................................
...................................................................................................................................................................................................................................................

2 0 
 0 −3



m
10 
=  
n
 
1

‫اﻣﺘﺤﺎن أم اﻟﻘﯿﻮﯾﻦ 9002 / 0102 م‬

: ‫ ﺇﺫﺍ ﻛﺎﻥ‬m , n ‫)51( ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛﻼﹰ ﻣﻦ‬

..........................................................................................................................................................................................................................................
..........................................................................................................................................................................................................................................
..........................................................................................................................................................................................................................................

 


41

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‫ ﺟﻮاھﺮ اﻟﺮﯾﺎﺿﯿﺎت‬‫إﻋﺪاد / ﻋﺎدل ﺣﺴـــــــﯿﻦ‬

‫اﻟﺤﺎدي‬

2
, B= 
 −1

‫ﻋاﻟﻌﻠﻤﻲ اﻟﻔﺼﻞ اﻟﺪراﺳﻲ اﻷول‬
‫ﺸ‬
‫ﺮ‬

6 −3
A=

5 −2 …...

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