B matritsalar

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

5 1 −2 3 5 5

𝐴 = [
1 3 −1^{], 𝐵 = [}7 1 2 ^]

8 4 −1 1 6 10

4. 
   Berilgan determinant uchun
   

a₁₂ va
^a34
elementlarining minor va algebraik

to’ldiruvchilarni toping.Berilgan determinantni hisoblang: a) 1- satr elementlari
bo’yicha yoyib b) 4- ustun elementlari bo’yicha yoyib v) oldindan 1- satr elimentlarini nollarga aylantirib

1 8	2	 3
3  2	0	4
5  3	7	1
3 2	0	2

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.


^{4x1  x2  4x3  19}
1. _2x₁  x₂  2x₃  11
^{3x1  x2  2x3  1}


2. _2x₁  2x₂  3x₃  9

^x  x  2x  8
^x  x  x  2

 1 2 3  1 2 3

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   


^{2x1  x2  x3  0}
1. _3x₁  2x₂  4x₃  0
<sup>x1  2x2  5x3  0

</sup> 1 2 3
2. ^x  2x  4x  0

^x  5x  3x  0 ^2x  9x  0
 ^{1 2 3}  ^{1 3}

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

Quyidagilarni hisoblang:

1. 
   a, 2b,3c
   

2. 
   3a,  7b
   

uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping;

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

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

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

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

• 
  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?

14. Variant

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

  A    B

matritsani toping:

 ^{1 3 2} 
 
 ^{1 0 2} 
 

A  _ 3 0 3 _ , B  _ 0 1 3 _
  2
  3

1

0

0

2

2

1
   
   

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

 ^{2 4}   ^{1 2} 

A  ^{ } ,
_ 0 3 _
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	2	5	1	−1	1
𝐴 = [	3	3	6^]^,	^𝐵^=^[2	3	3^]
	4	3	4	1	−2	−1

4. 
   Berilgan determinant uchun
   

a₂₂ va
^a34
elementlarining minor va algebraik

to’ldiruvchilarni toping.Berilgan determinantni hisoblang: a) 2- satr elementlari

bo’yicha yoyib b) 4- ustun elementlari bo’yicha yoyib v) oldindan 1- satr elimentlarini nollarga aylantirib

2  3	4	1
4  2	3	2
3 0	2	1
3 1	4	3

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.

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


2. _9x₁  4x₂  7x₃  3

^x  x  2x  4
^3x  x  2x  5

 ^{1 2 3}  ^{1 2 3}

4. 
   Bir jinsli tenglamalar sistemasini yeching:
   


^{4x1  x2  3x3  0}
1. _8x₁  x₂  7x₃  0
<sup>x1  3x2  5x3  0

</sup> 1 2 3
2. ^x  2x  3x  0

^2x  4x  5x  0 ^2x  x  2x  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?

15. Variant

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

  A    B

matritsani toping:

 ⁰
A  ^
_ 1
^{2 1} 
 ,
1 3 _
 ¹
B  ^
_ 0
^{3 2} 

1 3 _
  3
  2

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

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

1 −2 5 −1 1 1

^{𝐴 = [}3 0 6^{], 𝐵 = [}
4 3 4
2 3 3 ^]
1 −2 −1

4. 
   Berilgan determinant uchun
   

a₁₂ va
^a33
elementlarining minor va algebraik

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

3 1	2	3
4 1	2	4
1 1	1	1
4 1	2	5

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  2x3  8} ^{8x1  x2  3x3  2}

1. 
   ^x  x
   

• 
  2x
  

 11

2. 
   4x  x
   

 6x  1

^ 1 2 3 ^ 1 2 3

^4x  x

• 
  4x
  

 22
^4x

• 
  2x
  

 3x  7

 1 2 3  1 2 3

6.Bir jinsli tenglamalar sistemasini yeching:

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


2. _3x₁  2x₂  3x₃  0

^x  7x  2x  0 ^5x  x  x  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?