B matritsalar

1. ^Variant

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

  A    B

matritsani toping:

 ^{1 1
1} 
 ^{2 3
1}





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

2. 
   𝐴 va 𝐵 matritsalar berilgan. A B matritsani toping.
   

 ^{2 0} 
 ^{1 1
1} 



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

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

A B
b) 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
a₄₂ va
^a31
elementlarining minor va algebraik

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

1	1	 2	0
3	6	 2	5
1	0	6	4
2	3	5	1

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  7}
1. _2x₁  3x₂  x₃  1
^{3x1  2x2  4x3  8}


2. _2x₁  4x₂  5x₃  11

^3x  2x  x  6 ^x  2x  x  1
 ^{1 2 3}  ^{1 2 3}

5. 
   Bir jinsli chiziqli tenglamalar sistemasini yeching:
   

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


2. _3x₁  2x₂  x₃  0

^4x 11x  10x  0 ^8x  x  3x  0
 ^{1 2 3}  ^{1 2 3}

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

Quyidagilarni hisoblang:

1. 
   a,3b, c
   

2. 
   3a, 2c
   

^v) b,  4c

g) a va c

uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping; ikki vektorni skalyar ko’paytmasini hisoblang .

ikki vektor ortogonalmi yoki koolleniarmi tekshiring?

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

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

6. 
   va D(3;  6;  3) ^nuqtalarda
   

yotadi.Quyidagilarni hisoblang:

1. 
   Ko’rsatilgan ACD yog’ini yuzini b) Piramidaning ikki C va D
   

uchlari va
L  AB

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

2. Variant

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

  A    B

matritsani toping:

 ^{1 1} 
 
 ^{2 3} 
 

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

3

2

3

1
  
   




 ^{2 0} 
 ^{1 1} 

2. 
   𝐴 va 𝐵 matritsalar berilgan. A B
   

matritsani toping. A  ^ _{1 3} ^ ,
B  ^{ }
_ 3 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}

𝐴 = [

3 5 −6
2 4 3
2 8 −5
^{], 𝐵 = [}−3 −1 0^]

−3 1 1 4 5 −3

4. 
   Berilgan determinant uchun
   

a₃₂ va
^a33
elementlarining minor va algebraik

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

2 0 1 3
6 3  9 0
0 2 1 3
4 2 0 6

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  3} ^{x1  x2  x3  1}

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

^4x  x

• 
  4x
  

 3
^2x

• 
  3x
  

 2

 ^{1 2 3}  ^{1 3}

4. 
   Bir jinsli tenglamalar sistemasini yeching:
   

<sup>3x1  x2  2x3  0

</sup> 1 2 3
1. ^x  x  x  0
^{5x1  6x2  4x3  0}


2. _3x₁  3x₂  x₃  0

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

7. a  3i  4 j  k ,
b  i  2 j  7k va c  3i  6 j  21k
vektorlar berilgan.

Quyidagilarni hisoblang:

1. 
   5a, 2b, c
   

2. 
   4b, 2c
   

uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping;

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

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

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

8.Piramidaning uchlari
A (  7;  5; 6), B(  2 ; 5;  3),C (3;  2; 4) va D(1;
2; 2)

nuqtalarda yotadi.Quyidagilarni hisoblang:

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

A va B
uchlari va
L  CD

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

3. Variant

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

  A    B

matritsani toping:

 ^{2 1 3} 
 
 ^{2 3 0} 
 

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

3

2

1

3
  
  
1 2 _

2. 
   𝐴 va 𝐵 matritsalar berilgan. A B matritsani toping.
   

 ^{2 0 1} 
 
 ^{1 1 2} 
 

A  _ 1 3 3 _ B  _ 3 2 1 _

2

0

2

2

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}

2 1 −1 3 6 0

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

4. 
   Berilgan determinant uchun
   

a₄₂ va
^a31
elementlarining minor va algebraik

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

2	7 2	1
1	1 1	0
3	4 0	2
0	5 1	 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.

<sup>3x1  x2  x3  12

</sup> 1 2 3
1. ^x  2x  4x  6
^{2x1  x2  4x3  15}


2. _3x₁  x₂  x₃  8

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

4. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _2x₁  4x₂  x₃  0

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

4.