B matritsalar


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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


      1. 𝐴 va 𝐵 matritsalar berilgan.

AB
matritsani toping.





,
2 4
A
3 3
1 2
 


B 2 1

3


1

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

AB

    1. B A

v) A 1

g) A A1 d) A1A


6 7 3 2 0 5


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



  1. 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




  1. 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

    1. 2x

  • 3x

 4x  6

1 2 3 1 2 3

8x

  • 3x

  • 6x

 12
2x

  • 4x

 2x  2

 1 2 3  1 2 3



  1. 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;




  1. 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?
  1. 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




    1. 𝐴 va 𝐵 matritsalar berilgan.

AB
matritsani toping.


2 4


1 2
 

A ,
3 1
B 0 1

2




1


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

AB

  1. B A

v) A 1




g) A A1

d)

A1A
















−2

3

4

3

3

1










𝐴 = [

8

−1

−4],

𝐵 = [0

6

2]













−1

2

2

1

9

2




  1. 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




  1. 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?
  1. 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

  1. 𝐴 va 𝐵 matritsalar berilgan.

AB
matritsani toping.




,
2 4
A
1 3
2 2
 


B 3 1

2


0


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

AB

  1. B A

v) A 1




g) A A1

d) A1 A













1

7

3




6

5

2







𝐴 = [

−4

9

4]

,

𝐵 = [1

9

2]










0

3

2




4

5

2




  1. 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




  1. 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



  1. 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 uch vektorni aralash ko’paytmasini toping;

  1.  8b,5c 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?

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