B matritsalar

22 -Variant

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

  A    B

matritsani toping:

 ^{ 2
1 2} 
 ^{3 2 4} 

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

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

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


B  _ 2 1 _

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 7 3 2 0 5
^{𝐴 = [} 3 1 0^{], 𝐵 = [}4 −5 −2^]
2 2 1 4 3 7

4. 
   Berilgan determinant uchun
   

a₂₂ va
^a33
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- satr elimentlarini nollarga aylantirib

2 1	2	0
3 4	1	2
2 1	0	1
1 2	3	 2

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.




^{4x1  x2  3x3  9} ^{4x1  7x2  2x3  0}

1. 
   ^x  x  x
   

 2

2. 
   2x
   

• 
  3x
  

 4x  6

^ 1 2 3 ^ 1 2 3

^8x

• 
  3x
  

• 
  6x
  

 12
^2x

• 
  4x
  

 2x  2

 1 2 3  1 2 3

4. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _3x₁  3x₂  5x₃  0

^3x  2x  0
^4x  x  6x  0

 ^{1 3}  ^{1 2 3}

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

Quyidagilarni hisoblang:

1. 
   7a,  4b, 2c uch vektorni aralash ko’paytmasini toping;
   

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

v) 2b
va 4c
ikki vektorni skalyar ko’paytmasini hisoblang .

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

d) 7a, 2b, 5c uch vektorning komplanarligini tekshiring.

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

yotadi.Quyidagilarni hisoblang:

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

uchlari va
L  AD

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

23. Variant

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

  A    B

matritsani toping:

 ^1



A  _  3
_ 2
^{3 2} 



1 3 _ ,

2
4 _
 ^{3 0 4} 
 




B  _ 0 1 5 _
 1 0 4 _

  2

  1

2. 
   𝐴 va 𝐵 matritsalar berilgan.
   

A B
matritsani toping.

 ^{2 4} 

 ^{1 2} 
 

A  ^{ } ,
_ 3 1 _
B  _ 0 1 _

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	3	4	3	3	1
		𝐴 = [	8	−1	−4^]^,	^𝐵^=^[0	6	2^]
			−1	2	2	1	9	2

4. 
   Berilgan determinant uchun
   

a₃₂ va
^a31
elementlarining minor va algebraik

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

3	2	0	 2
1	1	2	3
4	5	1	0
1	2	3	 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  3x2  4x3  33} ^{5x1  9x2  4x3  6}

1. ^

• 
  5x
  

 24
2. ^x

• 
  7x
  

 5x  1

^7x1 2 ^ 1 2 3

^4x
11x
 39
^4x
 2x  x  2

 ^{1 3}  ^{1 2 3}
6.Bir jinsli tenglamalar sistemasini yeching:
^{2x1  x2  5x3  0} ^{2x1  x2  3x3  0}
1. ^x  2x  3x  0 2. ^x  2x  4x  0
^ 1 2 3 ^ 1 2 3
^5x  x  4x  0 ^x  x  x  0
 ^{1 2 3}  ^{1 2 3}

^7. a  9i  3 j  k ,
b  3i 15 j  21k
va c  i  5 j  7k
vektorlar berilgan.

Quyidagilarni hisoblang:

a) 2a,  7b,3c
b)  6a, 4c
uch vektorni aralash ko’paytmasini toping;
ikki vektorni vektor ko’paytmasini modulini toping;

^v) 5b
va 7a
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 (5;  4; 4), B(  4 ;  6;
5),C (3; 2;  7) va D( 6; 2;
 9)

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?

23. 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 _

 ^{2 2} 

 


B  _ 3 1 _



2
_{ 0} 

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	7	3		6	5	2
			𝐴 = [	−4	9	4^]	,	^𝐵^=^[1	9	2^]
				0	3	2		4	5	2

4. 
   Berilgan determinant uchun
   

a₄₂ va
^a33
elementlarining minor va algebraik

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

0	4	1 1
 4	2	1 3
0	1	2  2
1	3	4  3

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  3x2  4x3  12}
1. _7x₁  5x₂  x₃  33
^{x1  5x2  x3  3}


2. _3x₁  2x₂  x₃  7

^4x  x  7
^4x  3x  1

 ^{1 3}  ^{1 2}

6. 
   Bir jinsli tenglamalar sistemasini yeching:
   

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


2. _4x₁  x₂  5x₃  0

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

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

Quyidagilarni hisoblang:

1. 
   a,  6b, 2c
   

2. 
    8b,5c
   

uch vektorni aralash ko’paytmasini toping;

ikki vektorni vektor ko’paytmasini modulini toping;

v) 7c
va  9a
ikki vektorni skalyar ko’paytmasini hisoblang .

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

^d) a,  6b, 5c ^{uch vektorning komplanarligini tekshiring.}

8.Piramidaning uchlari
A (  7;  6;  5), B( 5 ; 1;
 3),C (8; 4; 0) va D(3; 4;
 7)

nuqtalarda yotadi.Quyidagilarni hisoblang:

1. 
   ^{Ko’rsatilgan} BCD ^{yog’ini yuzini b) Piramidaning ikki} B va C
   

uchlari va
L  AD

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

23.