B matritsalar

Variant

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

  A    B

matritsani toping:

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

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

 ^{1 3 1} 
 
 ^{3 2 0} 
 




A  _ 2 3 2 _ ,

2
_ 1 0 _
B  _ 2 1 2 _

4




_ 0 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 6 1 4 −3 2

𝐴 = [
1 3 2^{], 𝐵 = [}−4 0 4^]

0 1 1 3 2 −3

4. 
   Berilgan determinant uchun
   

a₄₂ va
^a32
elementlarining minor va algebraik

to’ldiruvchilarni toping. Berilgan determinantni hisoblang: a) 4- satr elementlari bo’yicha yoyib b) 2- ustun elementlari bo’yicha yoyib v) oldindan 1- satr elimentlarini nollarga aylantirib

0	 2	1	7
4	 8	2	 3
10	1	 5	4
 8	3	2	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.


^{x1  4x2  x3  6}
1. _5x₂  4x₃  20
<sup>5x1  5x2  4x3  3

</sup> 1 2 3
2. ^x  x  5x  1

^3x  2x  5x  22
^4x  4x  9x  0

 1 2 3  1 2 3

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _3x₁  2x₂  x₃  0

^x  x  5x  0 ^7x  x  3x  0
 ^{1 2 3}  ^{1 2 3}

7. a  9i  4 j  5k ,
b  i  2 j  4k
va c  5i 10 j  20k
vektorlar berilgan.

Quyidagilarni hisoblang:

a)  2a,7b,5c


b)  6b,7c
uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping;

v) 9a
va 4c
ikki vektorni skalyar ko’paytmasini hisoblang .

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

d)  2a, 7b, 4c uch vektorning komplanarligini tekshiring.

8.Piramidaning uchlari
A ( 7; 1;  2), B(1 ; 7;
8),C ( 3;7; 9) va D(  3;
 5;

2. 
   nuqtalarda
   

yotadi.Quyidagilarni hisoblang:

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

A va C
uchlari va
L  BC

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

11. Variant

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

  A    B

matritsani toping:

 ^{1 3 2}   ^{3 2 4} 

A  ^{ } ,
_ 3 1 3 _
B  ^
_ 1

1 5 _
  2
  3

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

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

6	9	4	1	1	1
^𝐴^=^[−1	−1	1^]^,	^𝐵^=^[3	4	3	]
10	1	7	0	5	1

4. 
   Berilgan determinant uchun
   

a₃₂ va
^a34
elementlarining minor va algebraik

to’ldiruvchilarni toping.Berilgan determinantni hisoblang: a) 3- satr elementlari
bo’yicha yoyib b) 4- ustun elementlari bo’yicha yoyib v) oldindan 1- satr elimentlarini nollarga aylantirib


5  3 7 1
3 2 0 2
2 1 4  6
3  2 9 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  21}
1. _3x₁  4x₂  2x₃  9
^{7x1  2x2  x3  2}


2. _6x₁  4x₂  5x₃  3

^2x  x  x  10
^x  2x  4x  5

 ^{1 2 3}  ^{1 2 3}

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _2x₁  3x₂  5x₃  0

^x  3x  4x  0 ^5x  x  4x  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?

12. Variant

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

  A    B

matritsani toping:

 ^{1
2 0} 
 ^{3 2 4} 

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

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

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


B  _ 2 4_



0
_{ 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	0	3	3	5	4
^𝐴^=^[3	1	7^]^,	^𝐵^=^[−3	0	1^]
2	1	8	5	6	−4

4. 
   Berilgan determinant uchun
   

a₁₂ va
^a32
elementlarining uchun 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

4	1	1	5
0	2	 2	3
3	4	1	2
4	1	1	 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.




^{3x1  2x2  5x3  5} ^{4x1  3x2  x3  3}
1. 2x  3x  4x  12 2. ^x  x  x  4
^ 1 2 3 ^ 1 2 3

^x  2x

• 
  3x
  

 1
^3x

• 
  4x
  

 2x  2

 ^{1 2 3}  ^{1 2 3}

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _3x₁  2x₂  3x₃  0

^3x  2x  5x  0 ^2x  x  x  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?

13.