Vektor boshining koordinatalari
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va b vektorlar orasidagi burchak / 4
ga teng va 2 a , 3 b ekanligi ma’lum bo‘lsa 2 3
a b vektorning uzunligini hisoblang.
1
3 2 5
6 4 5 7
A
matritsani elementar almashtirishlar yordamida zinapoya ko‘rinishga keltiring.
Ikki a va b vektorlar orasidagi burchak / 6
ga teng va 3 a , 3 b ekanligi ma’lum bo‘lsa 2 3
a b vektorning uzunligini hisoblang.
1 2 3
3 5 6 3 2 7
A
matritsani elementar almashtirishlar yordamida zinapoya ko‘rinishga keltiring.
Ikki a va b vektorlar orasidagi burchak / 3
ga teng va 2 a , 3 b ekanligi ma’lum bo‘lsa 2 3
a b vektorning uzunligini hisoblang.
1
3 6 11 6
3 7 7 A
matritsani elementar almаshtirishlar yordamida zinapoya ko‘rinishga keltiring.
Ikki a va b vektorlar orasidagi burchak / 3
ga teng va 4 a , 2 b ekanligi ma’lum bo‘lsa 2 3
a b vektorning uzunligini hisoblang.
1
3 5 11 6
3 9 7 A
matritsani elementar almаshtirishlar yordamida zinapoya ko‘rinishga keltiring.
Ikki a va b vektorlar orasidagi burchak / 4
ga teng va 2 a , 2 2 b ekanligi ma’lum bo‘lsa 2 3
a b vektorning uzunligini hisoblang.
1
3 3 1 6 5 15 8
A
matritsani elementar almаshtirishlar yordamida zinapoya ko‘rinishga keltiring.
Agar 7 2 , 4
b va
0 , ^ 45 a b bo‘lsa, 3a b va 2
b
ning qanday qiymatlarida o‘zaro
perpendikulyar bo‘ladi?
1 2 3 2 5 6
va 2 1 1 3 2 4 B matritsalar berilgan bo’lsa,
A B ni toping. Agar
2, 4
b va
0 , ^ 60 a b bo‘lsa, 3a b va 2
b
ning qanday qiymatlarida o‘zaro
perpendikulyar bo‘ladi?
1 2 3 2 5 6
va 1 1 1 2 2 3 B matritsalar berilgan bo’lsa,
A B ni toping. Agar
2, 2 3
a b va
0 , ^ 30 a b bo‘lsa, 3a b va 2
b
ning qanday qiymatlarida o‘zaro
perpendikulyar bo‘ladi
2 2 3 2 1 1 A va 2 1 1 3 2 4
matritsalar berilgan bo’lsa,
A B ni toping.
Agar
3, 2 3
a b va
0 , ^ 30 a b bo‘lsa, 3a b va 2
b
ning qanday qiymatlarida o‘zaro
perpendikulyar bo‘ladi?
1 2 3 2 5 6
va 2 1 1 3 2 2 B matritsalar berilgan bo’lsa,
A B ni toping. Agar
2 , 2
b va
0 ,^ 45 a b bo‘lsa, 3a b va 2
b
ning qanday qiymatlarida o‘zaro
perpendikulyar bo‘ladi?
1 2 2 2 5 6
va 2 1 1 3 2 4 B matritsalar berilgan bo’lsa,
A B ni toping. Uchlari
A 2;3;1 , B 2; 1;4 va
2; 4;0 C
nuqtalarda bo‘lgan uchburchak berilgan. Bu uchburchakning
ichki
burchagini hisoblang.
1 2 2 2 5 6
va 2 1 1 3 3 4 B matritsalar berilgan bo’lsa, A B ni toping. Uchlari
A 3;11;3 , B 3;7;6 va
C
nuqtalarda bo‘lgan uchburchak berilgan.
Bu uchburchakning C
ichki burchagini hisoblang.
3 1 2 2 5 6
A va
2 1 1 3 2 4
matritsalar berilgan bo’lsa, A B ni toping. Uchlari
A 5;10;2 , B 5;6;5 va
C
nuqtalarda bo‘lgan uchburchak berilgan.
Bu uchburchakning C
ichki burchagini hisoblang
1 2 2 2 5 6
va 2 1 1 3 2 1 B matritsalar berilgan bo’lsa,
A B ni toping. Uchlari
A 2;8;2 , B 2;4;5 va
C
nuqtalarda bo‘lgan uchburchak berilgan.
Bu uchburchakning C
ichki burchagini hisoblang.
1 2 2 2 5 6
va 2 1 1 2 2 1 B matritsalar berilgan bo’lsa,
A B ni toping. Дан треугольник с вершинами
A 3;9;4 , B 3;5;7 и
C . Найти внутренная угол при вершине C .
1 2 2 2 1 2
va 2 1 1 3 2 4 B
matritsalar berilgan bo’lsa,
A B ni toping. ) 3 , 1 , 3 ( ), 6 , 4 , 3 ( ), 3 , 2 , 1 ( C B A нуқталар berilgan bo‘lsa, AB va AC vektorlar orasidagi burchak kosinusini toping
Determinantni hisoblang 1 2 3 2 1 3 3 3 1 (2,3,4),
(2,4,6), ( 3,2,3) A B C
berilgan bo‘lsa,
AB va AC vektorlar orasidagi burchak
kosinusini toping
Determinantni hisoblang 2 2 3 2 2 3 3 3 2 (3,2,4),
(2,5,6), (6,7,8) A B C
berilgan bo‘lsa, AB va AC vektorlar orasidagi burchak
kosinusini toping
Determinantni hisoblang 2 2 1 2 1 3 1 3 2 (1,2,4),
(2,5,6), (3,7,5) A B C
berilgan bo‘lsa, AB va AC vektorlar orasidagi burchak
kosinusini toping
Determinantni hisoblang 2 2 2 2 2 3 2 3 2 (1,2,4),
(2,2,6), (3,3,5) A B C
berilgan bo‘lsa, AB va AC vektorlar orasidagi burchak
kosinusini toping
Determinantni hisoblang 2 1 1 1 2 3 2 3 2
Savol Savol 1 2 3 1 2 3 1 2 3 2 3, 2 2 1, 3 6.
x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ?
Agar kvadrat
matritsaning bosh
diagonalidan tashqari barcha elementlari nollardan iborat bo`lsa, u qanday ataladi?
1
3 1 2 3 1 2 3 2 2, 2 2 3 3, 2 2 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
Agar
kvadrat matritsaning bosh diagonalidan pastdagi barcha elementlari nollardan iborat bo`lsa, u qanday ataladi?
1 2 3 1 2 3 1 2 3 2 8, 2 3 10, 2 3 4 4.
x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
Agar
kvadrat matritsaning bosh diagonalidan yuqoridagi barcha
elementlari nollardan iborat bo`lsa, u qanday ataladi? 1 2
1 2 3 1 2 3 2 7 10, 2 2, 3 5 3 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
ifodasidagi U qanday matritsa bo`ladi? 1 2 3 1 2 3 1 2 3 2 3 5, 3 2 3 1, 2 3 2 8. x x x x x x x x x Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
ifodasidagi L qanday matritsa bo`ladi? 1 2 3 1 2 3 1 2 2 6, 4 5 6 9, 7 8 6. x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ? x ni Kramer usulida toping A kvadrat
matritsaning LDU A
ifodasidagi D qanday matritsa bo`ladi? 1 2 3 1 2 3 1 2 3 2 3 13, 2 2, 3 4 7. x x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ? x ni Kramer usulida toping 3 0 0 4 1 0 3 2 3 qanday matritsa?
1 2 3 1 2 3 1 2 3 3 2 3 1, 2 2 4, 3 9.
x x x x x x x x
3 0 1 0 1 0 1 0 3 qanday matritsa?
Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
2 3 1 2 3 1 2 3 2 3, 2 2 1, 3 6. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Quyidagilardan qaysi biri L matritsa bo`ladi? 1 5 0 1 , 3 1 1 0 , 1 0 5 1 , 0 3 2 1 . 1 2 3 1 2 3 1 2 3 2 2, 2 2 3 3, 2 2 5.
x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Quyidagilardan qaysi biri U matritsa bo`ladi? 1 0 3 1 , 1 3 0 1 , 5 1 1 0 , 0 1 1 4 . 1 2 3 1 2 3 1 2 3 2 8, 2 3 10, 2 3 4 4.
x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
4 3 2 A
va 1 3 2 B
matritsalar berilgan bo`lsa, A B ni hisoblang. 1 2 3 1 2 3 1 2 3 2 7 10, 2 2, 3 5 3 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
4 0 4 3 1 2
va
2 0 1 3 1 2 B
matritsalar berilgan bo`lsa, B A ni hisoblang. 1 2 3 1 2 3 1 2 3 2 3 5, 3 2 3 1, 2 3 2 8. x x x x x x x x x Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
4 0 4 3 1 2
va
2 0 1 3 1 2 B
matritsalar berilgan bo`lsa, T T A B ni hisoblang. 1 2 3 1 2 3 1 2 3 2 2 8, 3 3, 3 2 2 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
4 0 4 3 1 2
va
2 0 1 3 1 2 B
matritsalar berilgan bo`lsa, A B ni hisoblang.
1 2 3 1 2 3 1 2 2 6, 4 5 6 9, 7 8 6. x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ? x ni Kramer usulida toping Agar
4 3 2 A
va 1 3 2 B
matritsalar berilgan bo`lsa, A B ni hisoblang.
1 2 3 1 2 3 1 2 3 2 3 13,
2 2, 3 4 7.
x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ? x ni Kramer usulida toping Agar
4 3 2 A
va 1 3 2 B
matritsalar berilgan bo`lsa, B A ni hisoblang. 1 2 3 1 2 3 1 2 3 3 2 3 1, 2 2 4, 3 9. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
4 2 6 3 1 5
va
2 3 1 B
matritsalar berilgan bo`lsa, B A ni hisoblang. 1 2 3 1 2 3 1 2 3 2 3, 2 2 1, 3 6.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
Agar
4 2 6 3 1 5
va
2 3 1 B matritsalar berilgan bo`lsa, T T A B ni hisoblang.
1 2 3 1 2 3 1 2 3 2 2, 2 2 3 3, 2 2 5.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
1 0 0 4 1 0 3 2 1 matritsa LDU A
yoyilmaning qaysi matritsasi bo`la oladi? 1 2 3 1 2 3 1 2 3 2 8, 2 3 10, 2 3 4 4. x x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
4 1 3 0 3 4 0 0 1 matritsa LDU A
yoyilmaning qaysi matritsasi bo`la oladi? 1 2 3 1 2 3 1 2 3 2 7 10, 2 2, 3 5 3 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
1 4 3 0 1 5 0 0 1
matritsa LDU A
yoyilmaning qaysi matritsasi bo`la oladi?
1 2 3 1 2 3 1 2 3 2 3 5, 3 2 3 1, 2 3 2 8. x x x x x x x x x Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
4 0 0 1 3 0 3 4 1 matritsa LDU A
yoyilmaning qaysi matritsasi bo`la oladi?
1 2 3 1 2 3 1 2 3 2 2 8, 3 3, 3 2 2 5.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
Agar
4 0 4 3 1 2
va
2 0 1 3 1 2 B
matritsalar berilgan bo`lsa, B A ni hisoblang. 1 2 3 1 2 3 1 2 2 6, 4 5 6 9, 7 8 6. x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x
Agar
ij a A kvadrat matritsa bo`lib, ixtiyoriy j i lar uchun 0
a bo`lsa, A matritsa qanday ataladi?
1 2 3 1 2 3 1 2 3 2 3 13,
2 2, 3 4 7.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x ni Kramer usulida toping Agar
ij a A kvadrat matritsa bo`lib, ixtiyoriy j i lar uchun 0
a bo`lsa, A matritsa qanday ataladi? 1 2 3 1 2 3 1 2 3 3 2 3 1, 2 2 4, 3 9. x x x x x x x x x
3 ? x ni Kramer usulida toping Berilgan
7 4 6 2 A
matritsani LDU ko`paytmaga yoying.
1 2 3 1 2 3 1 2 3 3 2 1, 3 2 7, 2 3 6.
x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ? x ni Kramer usulida toping Agar
4 0 1 3 2 1
va
2 0 1 2 3 1 B
matritsalar berilgan bo`lsa, ) det(
B A ni hisoblang
1 2 3 1 2 3 1 2 3 3 2 1, 3 2 7, 2 3 6.
x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ? x ni Kramer usulida toping Agar
4 0 4 3 1 2
va
2 0 1 3 1 2 B atritsalar berilgan bo`lsa,
A det ni hisoblang
. 1 2 3 1 2 3 1 2 3 3 2 1, 3 2 7, 2 3 6.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x ni Kramer usulida toping Agar
0 3 2 1 1 2 A 1 4 0 5 2 3
va matritsalar berilgan bo`lsa,
B det ni hisoblang
Tenglamalar sistemasi berilgan. 1 2 3 1 2 3 1 2 3 2 2 3, 2 4, 4 4 3.
x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ? x ni Kramer usulida toping Berilgan
7 4 6 2 A
matritsani LU ko`paytmaga yoying 1 2 3 1 2 3 1 2 3 2 2 3, 2 4, 4 4 3. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ? x ni Kramer usulida toping Berilgan
7 4 6 2 A
matritsani LDU ko`paytmaga yoying
1 2 3 1 2 3 1 2 3 2 2 3, 2 4, 4 4 3. x x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x ni Kramer usulida toping Agar
4 3 5
va
1 3 2
matritsalar berilgan bo`lsa,
A det ni hisoblang.
1
3 1 2 3 1 2 3 3 11, 5 2 8, 2 4 16. x x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ?
ni Kramer usulida toping
Agar
2 1 7
va
1 3 4
matritsalar berilgan bo`lsa,
A det ni hisoblang.
1
3 1 2 3 1 2 3 3 11, 5 2 8, 2 4 16. x x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ?
ni Kramer usulida toping
Agar A kvadrat matritsa va I birlik matritsalardan tuzilgan A/I matritsani Gauss-Jordan usuli bilan I/B matritsaga keltirilgan bo`lsa, quyidagi tasdiqlardan qaysi biri o`rinli? B matritsa A matritsaga teskari matritsa; B - simmetrik matritsa; B matritsa A matritsaning transponirlangani 1 2 3 1 2 3 1 2 3 3 11, 5 2 8, 2 4 16. x x x x x x x x x
Agar 7 2 4 1 A matritsa berilgan bo`lsa,
Berilgan tenglamalar sistemasidan 3 ?
ni Kramer usulida toping
Jordan
usulida B I /
matritsaga keltiring(I-birlik matritsa) 1 2 3 1 2 3 1 2 3 3 1, 2 7, 2 3 5.
x x x x x x x x
Berilgan tenglamalar sistemasidan 2 ? x ni Kramer usulida toping Agar
2 3 1 2 A matritsa berilgan bo`lsa,
Jordan
usulida B I /
matritsaga keltiring(I-birlik matritsa)
1 2 3 1 2 3 1 2 3 3 1, 2 7, 2 3 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 1 ? x ni Kramer usulida toping Agar
3 1 2 1 A matritsa berilgan bo`lsa,
Jordan
usulida B I /
matritsaga keltiring(I-birlik matritsa)
1 2 3 1 2 3 1 2 3 3 1, 2 7, 2 3 5. x x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x ni Kramer usulida toping 1 6 4 6 1 3 0 1 1 A
matritsaning LU ko`paytma shaklidagi U matritsani aniqlang
1 2 3 1 2 3 1 2 3 3 1, 2 7, 2 3 5.
x x x x x x x x
Berilgan tenglamalar sistemasidan 3 ? x ni Kramer usulida toping 2 4 1 2 7 2 1 3 1 A
matritsaning LU ko`paytma shaklidagi
aniqlang 1 2
4 2 3 4 1 3 4 1 2 3 2 2 4 3 1 2 0 3 4 2
x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
1
x ni Gauss usulida toping Agar
2 4 1 2 7 2 1 3 1
matritsa berilgan bo`lsa,
I A/ matritsani tuzing va Gauss- Jordan
usulida 1 / A I
matritsaga keltiring(I-birlik matritsa). 1 2 4 1 2 3 4 2 3 4 1 2 3 2 4 2 2 1 3 2 5 3 2 3 x x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
1
x ni Gauss usulida toping Berilgan
2 4 1 2 7 2 1 3 1
matritsani LU ko`paytmaga yoying
1 2 3 4 2 3 4 1 3 4 1 2 3 2 2 4 3 1 2 0 3 4 2 x x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
2
x ni Gauss usulida toping Berilgan
1 3 3 6 5 2 2 4 1
matritsani LU ko`paytmaga yoying
1 2 4 1 2 3 4 2 3 4 1 2 3 2 4 2 2 1 3 2 5 3 2 3
x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
2
x ni Gauss usulida toping Berilgan
3 7 2 6 0 3 4 1 1 A
matritsani LU ko`paytmaga yoying. 1 2 3 4 2 3 4 1 3 4 1 2 3 2 2 4 3 1 2 0 3 4 2 x x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
3
x ni Gauss usulida toping 1 6 4 6 1 3 0 1 1 A
matritsaning LU ko`paytma shaklidagi
aniqlang.
.
2 4 1 2 3 4 2 3 4 1 2 3 2 4 2 2 1 3 2 5 3 2 3
x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
3
x ni Gauss usulida toping 3 7 4 6 0 6 4 1 2 A
matritsaning LU ko`paytma shaklidagi L matritsani aniqlang
1 2 3 4 2 3 4 1 3 4 1 2 3 2 2 4 3 1 2 0 3 4 2 x x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
4
x ni Gauss usulida toping Agar A kvadrat matritsa va I birlik matritsalardan tuzilgan A/I matritsani Gauss-Jordan usuli bilan I/B matritsaga keltirilgan bo`lsa, quyidagi tengliklardan qaysi biri o`rinli? I A B 1 1 ;
A B 1 ; I A B 1 ; A B T
Tenglamalar sistemasi berilgan. 1 2 4 1 2 3 4 2 3 4 1 2 3 2 4 2 2 1 3 2 5 3 2 3 x x x x x x x x x x x x x
Berilgan tenglamalar sistemasidan
4
x ni Gauss usulida toping Agar A kvadrat matritsa va I birlik matritsalardan tuzilgan A/I matritsani Gauss-Jordan usuli bilan I/B matritsaga keltirilgan bo`lsa, quyidagi tengliklardan qaysi biri noo`rin? 1 1
A B A B ;
B A 1 1 ; 1
B ;
A B A 1 1 . Tenglamalar sistemasini yeching. Agar A kvadrat matritsa va I birlik matritsalardan tuzilgan A/I matritsani
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2 3 8 3 8 0 3 7 3 16 x x x x x x x x x x x x x x x x
Gauss-Jordan usuli bilan I/B matritsaga keltirilgan bo`lsa, quyidagi tengliklardan qaysi biri noo`rin?
1 ; I B A 1 1
1
B ;
A B Tenglamalar sistemasini yeching. 1 2
4 1 2 3 4 1 2 3 4 1 2 3 2 3 5 1 2 3 2 5 3 5 7 9 10 8 5 2 x x x x x x x x x x x x x x x
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