B matritsalar

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Variant

Variant

3. A, B matritsalar va ^,  sonlar berilgan.
  A    B

matritsani toping:

 ¹^¹
^¹
 ²³
^¹





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

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

 ^{2 0}
 ¹^¹
^¹



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

𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)

A B

B  A

v) ^A^¹

g) ^A^^A^¹d) ^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
a₄₂va
^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

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.

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


2. _2x₁ 4x₂ 5x₃ 11

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

Bir jinsli chiziqli tenglamalar sistemasini yeching:

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

a,3b, c

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;

va D(3;  6;  3) nuqtalarda

yotadi.Quyidagilarni hisoblang:

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?

Variant

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

𝐴 va 𝐵 matritsalar berilgan. A B

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

𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)

A B

B  A

v) ^A^¹

g) ^A^^A^¹d) ^A^¹^^A

𝐴 = [

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

−3 1 1 4 5 −3

Berilgan determinant uchun

a₃₂va
^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

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.

²^x¹^^x²^²^x³^³^x¹^^x²^^x³^¹

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

^4x  x

 3
^2x

 2

 ^{1 2 3} ^{1 3}

Bir jinsli tenglamalar sistemasini yeching:

³^x¹^^x²^²^x³^⁰

^1 2 3
1. ^x  x  x  0
⁵^x¹^⁶^x²^⁴^x³^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:

5a, 2b, c

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:

^{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?

Variant

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 _

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

 ^{2 0}¹
 
 ¹^¹²
 

A  _1 3 3 _B  _3 2 1 _

2

0

2

2

4

2
   
  _, 

𝐴 va 𝐵 matritsalar berilgan.Quydagilarni toping: a)

A B

B  A

v) ^A^¹

g) ^A^^A^¹d) ^A^¹^^A

2 1 −1 3 6 0

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

Berilgan determinant uchun

a₄₂va
^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

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.