B matritsalar

19 -Variant

1. 
   A, B matritsalar ^ va  sonlar berilgan.
   

  A    B

matritsani toping:

 ^{1 3} 
 


A  _  3 1 _ ,

1


_{ 2} 
 ^{3 0} 
 




B  _ 0 1 _
 1 2 _

  4

  2

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

 ⁰

A  _ 3
¹ 


3 ^ ,

 ⁰

B  ^
3


^{2 2}

2 1

4

2
_{ }  
 

3. 
   𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)
   

A B

2. 
   B  A
   

v) ^{A 1}

g) ^A^^A^^1	d)	A^^1  A
−6	1	11	3	0	1
^𝐴^=^[9	2	5 ^]^,	^𝐵^=^[0	2	7^]
0	3	7	1	−3	2

4. 
   Berilgan determinant uchun
   

a₁₂ va
^a33
elementlari uchun minor va algebraik

to’ldiruvchilarni toping.Berilgan determinantni hisoblang: a) 1- satr elementlari bo’yicha yoyib b) 3- ustun elementlari bo’yicha yoyib v) oldindan 1- chi satr elimentlarini nollarga aylantirib

4	 5	1	 5
 3	2	8	 2
5	3	1	3
 2	4	 6	8

5. 
   Tenglamalar sistemasining birgalikda yoki birgalikda emasligini tekshiring.
   

Agar tenglamalar sistemasi birgalikda bo’lsa uni yeching: a) Kramer formulalari yordamida; b) Teskari matritsa usuli yordamida; v) Gauss usuli yordamida.




^{2x1  x2  3x3  4} ^{3x1  3x2  2x3  2}
1. ^x  3x  x  11 2. 4x  5x  2x  1
^ 1 2 3 ^ 1 2 3

^x  2x

• 
  2x
  

 7
^x  2x  5

 1 2 3  1 2

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   

^{4x1  x2  10x3  0} ^{x1  x2  x3  0}

1. ^x  2x  x  0 2. ^ x  3x  4x  0
2
^ 1 2 3 ^ 1 2 3
^2x  3x  4x  0 ^3x  2x  5x  0
 1 2 3  1 2 3

^7. a  7i  2k ,
b  2i  6 j  4k
va c  i  3 j  2k
vektorlar berilgan.

Quyidagilarni hisoblang:

1. 
   a,  2b,  7c ^{uch vektorni aralash ko’paytmasini toping;}
   

2. 
   4b,3c ^{ikki vektorni vektor ko’paytmasini modulini toping;}
   

^v) 2a
va  7c
ikki vektorni skalyar ko’paytmasini hisoblang .

^g) b va c ^{ikki vektor ortogonalmi yoki koolleniarmi tekshiring?}

d) 2a, 4b, 3c uch vektorning komplanarligini tekshiring.

8 .Piramidaning uchlari
A ( 2; 4; 1), B(  3;  2;
4),C ( 3; 5;  2) va D( 4;
2;  3)

nuqtalarda yotadi.Quyidagilarni hisoblang:

1. 
   Ko’rsatilgan ABD yog’ini yuzini b) Piramidaning ikki B va D
   

uchlari va
L  AC

qirrasining o’rtasidan o’tuvchi kesimining yuzasini toping. v) ABCD piramidaning hajmini toping?

20 -Variant

1. 
   A, B matritsalar ^ va  sonlar berilgan.
   

  A    B

matritsani toping:

 ^1



A  _  3
_ 2
^{3 1} 



1 2 _ ,

4
1 _
 ^{3 0 1} 
 




B  _ 0 1 0 _

2
_ 1 2 _

  4

  1

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B

 ¹

matritsani toping.




² 




A  _ 2
_ 4
3 ^ ,

4


 ⁰
B  ^
_ 3
^{2 2}

2 1 _

3. 
   𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)
   

A B

2. 
   B  A
   

v) ^{A 1}

g) ^{A  A1} d) ^{A1  A}

3 1 3 0 −1 2
^{𝐴 = [}−1 0 2^{], 𝐵 = [}2 1 1^]
1 2 1 3 7 1

4. 
   Berilgan determinant uchun
   

^a\ 22 ^va
a34
elementlarining minor va algebraik

to’ldiruvchilarni toping.Berilgan determinantni hisoblang: a) 2- satr elementlari bo’yicha yoyib b) 3- ustun elementlari bo’yicha yoyib v) oldindan 1- chi satr elimentlarini nollarga aylantirib

3	5	3	2
2	4	1	0
1	 2	2	1
5	1	 2	4

5. 
   Tenglamalar sistemasining birgalikda yoki birgalikda emasligini tekshiring.
   

Agar tenglamalar sistemasi birgalikda bo’lsa uni yeching: a) Kramer formulalari yordamida; b) Teskari matritsa usuli yordamida; v) Gauss usuli yordamida.


^{3x1  2x2  4x3  12}
1. _3x₁  4x₂  2x₃  6
^{3x1  2x2  4x3  8}


2. _2x₁  4x₂  5x₃  1

^2x  x  x  9
^5x  6x  9x  2

 ^{1 2 3}  ^{1 2 3}

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   


^{2x1  5x2  x3  0}
1. _4x₁  6x₂  3x₃  0
 ^{x1  2x2  4x3  0}


2. _5x₁  x₂  2x₃  0

^x  x  2x  0 ^4x  x  2x  0
 1 2 3  1 2 3

7. a  4i  2 j  k ,
b  3i  5 j  2k va c  j  5k
vektorlar berilgan.

Quyidagilarni hisoblang:

1. 
   a, 6b,3c
   

2. 
   2b va a
   

uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping;

v) a
va  4c
ikki vektorni skalyar ko’paytmasini hisoblang .

g) a va b

d) a, 6b, 3c

ikki vektor ortogonalmi yoki koolleniarmi tekshiring? uch vektorning komplanarligini tekshiring.

8.Piramidaning uchlari
A (  5;  3;  4), B(1 ; 4;
6),C (3; 2;  2) va D(8;
 2; 4)

nuqtalarda yotadi.Quyidagilarni hisoblang:

1. 
   ^{Ko’rsatilgan} ACD ^{yog’ini yuzini b) Piramidaning ikki}
   

A va D
uchlari va
L  BC

qirrasining o’rtasidan o’tuvchi kesimining yuzasini toping. v) ABCD piramidaning hajmini toping?

21-Variant

1. 
   A, B matritsalar ^ va  sonlar berilgan.
   

  A    B

matritsani toping:

 ^{1
3 2} 
 ^{3 0 4} 

A  ^{ } ,
_  3 1 3 _
B  ^
_ 0

1 5 _
  1
  3

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

,
 ^{2 4} 
A  ^{ }
_ 3 3 _
 ^{2 2}
B  ^{ }
_ 2 1_

3. 
   𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)
   

A B

2. 
   B  A
   

v) ^{A 1}

g) ^A^^A^^1	d)	A^^1  A
2	−1	−3	2	−1	−2
^𝐴^=^[8	−7	−6^]^,	^𝐵^=^[3	−5	4^]
−3	4	2	1	2	1

4. 
   Berilgan determinant uchun
   

a₁₂ va
^a32
elementlarining minor va algebraik

to’ldiruvchilarni toping. Berilgan determinantni hisoblang: a) 1- satr elementlari bo’yicha yoyib b) 2- ustun elementlari bo’yicha yoyib v) oldindan 1- satr elimentlarini nollarga aylantirib

3	2 0	 5
4	3  5	0
1	0  2	3
0	1  3	4

4. 
   Tenglamalar sistemasining birgalikda yoki birgalikda emasligini tekshiring.
   

Agar tenglamalar sistemasi birgalikda bo’lsa uni yeching: a) Kramer formulalari yordamida; b) Teskari matritsa usuli yordamida; v) Gauss usuli yordamida.

^{8x1  3x2  6x3  4} ^{3x1  x2  2x3  3}

1. ^x  x  x  2

2. 2x

• 
  2x
  

 5x  5

^ 1 2 3 ^ 1 2 3

^4x  x

• 
  3x
  

 5
^5x

• 
  3x
  

 7x  1

 1 2 3  1 2 3

4. 
   Bir jinsli tenglamalar sistemasini yeching:
   


^{3x1  x2  3x3  0}
1. _2x₁  3x₂  x₃  0
^{3x1  x2  x3  0}


2. _2x₁  3x₂  4x₃  0

^x  x  3x  0 ^5x  2x  3x  0
 ^{1 2 3}  ^{1 2 3}

^7. a  3i  2 j  k ,
b  2 j  3k va c  3i  2 j  k
vektorlar berilgan.

Quyidagilarni hisoblang:

1. 
   a,  3b, 2c ^{uch vektorni aralash ko’paytmasini toping;}
   

2. 
   5a, 3c ^{ikki vektorni vektor ko’paytmasini modulini toping;}
   

^v)  2a
va 4b
ikki vektorni skalyar ko’paytmasini hisoblang .

g) a va c ikki vektor ortogonalmi yoki koolleniarmi tekshiring?

d) 5a, 4b, 3c uch vektorning komplanarligini tekshiring.

8.Piramidaning uchlari
A (3; 4; 2), B(  2 ; 3;  5),C ( 4;  3; 6) va D( 6;
 5;

3. 
   ^nuqtalarda
   

yotadi.Quyidagilarni hisoblang:

1. 
   Ko’rsatilgan ABD yog’ini yuzini b) Piramidaning ikki
   

A va C
uchlari va
L  BD

qirrasining o’rtasidan o’tuvchi kesimining yuzasini toping. v) ABCD piramidaning hajmini toping?