Савол Савол Савол
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Yakuniy savollari II qism
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tashkil qiladimi: 1; 3;2 ,
4; 2;1 , 3;2;5 .
а b c
A sistemamatrisasi, B kengaytirilganmatrissabo’lsa, qachontenglamalarsistemasiyag onayechimgaega?
Agar kvadrat matritsaning bosh diagonalidan pastdagi barcha elementlari nollardan iborat bo`lsa, u qanday ataladi?
Berilgan vektorlar sistemasi bazis tashkil qiladimi: 2; 3;1 ,
1; 2;3 , 1;2;2 .
а b c
Chiziqlitenglamalarsistemasiya gonayechimgaegabo’lsa, u qandaynomlanadi?
LU A ifodasidagi U matritsa qanday
matritsa bo`ladi? Berilgan vektorlar sistemasi bazis tashkil qiladimi:
2; 4;1 , 2; 2;1 ,
1;2;2 . а b c
1 4 2 2 3 8 5 3
1 8 3 5 A matritsarangini toping.
LU A
ifodasidagi L matritsa qanday matritsa bo`ladi? Berilgan vektorlar sistemasi bazis tashkil qiladimi: 1; 4;4 ,
2;2;2 , 3;3;2 .
а b c
Chiziqlitenglamalarsistemasiya gonayechimgaegabo’lsa, u holdabusistema … deyiladi. A kvadrat
matritsaning LDU A ifodasidagi D matritsa qanday
matritsa bo`ladi? Berilgan vektorlar sistemasi bazis tashkil qiladimi:
2; 4;4 , 2;1;2 ,
3;3;0 . а b c
1 1 2 2 0 1 1 2 1 2 0 2 1 2 2 1
( ) rang B ni hisoblang
1 0 0 4 1 0 3 2 1 matritsa qanday ataladi?
Berilgan vektorlar sistemasi bazis tashkil qiladimi: 2; 4;1 ,
2;2;2 , 1;3;0 .
а b c
1 1 2 2 0 1 1 2 1 2 0 2 1 2 2 1
( ) T rang B ni hisoblang
Quyidagilardan qaysi biri elementar almashtirish? Berilgan vektorlar sistemasi bazis tashkil qiladimi:
2; 1;1 , 3;2;3 ,
1;3;0 . а b c
Chiziqlitenglamalarsistemasibir galikdabo’lishiuchunbusistema ningasosiy A vakengaytirilgan A matritsalariranglariorasidaqand ayshartbajarilishikerak?
Quyidagilardan qaysi biri elementar almashtirish emas? Berilgan vektorlar sistemasi bazis tashkil qiladimi: 2; 2;3 ,
0;2;3 , 1;2;1 .
а b c
2 1 0 1 1 1 3 2 1 4 2 0 B ( ) rang B ni hisoblang
Quyidagilardan qaysi biri L matritsa bo`ladi? Berilgan vektorlar sistemasi bazis tashkil qiladimi: 1; 2;3 ,
3;2;0 , 1;2;1 .
а b c
1 2 1 3 3 1 0 7 2 3 1 4 A ( )
rang A ni hisoblang
Quyidagilardan qaysi biri U matritsa bo`ladi? Berilgan vektorlar sistemasi bazis tashkil qiladimi: 3; 2;3 ,
2;3;1 , 3;2;2 .
а b c
1 3 2 2 1 3 1 0 1 3 7 4 T A
( ) T rang A ni hisoblang
Quyidagilardan qaysi biri A kvadrat matritsaning LDU A yoyilmasidagi L matritsa bo`la oladi? b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 2, 3,2 , 3,2,1 ,
4,1,2 , 1,2,3 .
а а а b
Tenglamlar sistemani yeching
0 3 2 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x .
Agar
4 0 1 3 2 1
va
2 0 1 2 3 1 B
matritsalar berilgan bo`lsa,
B A ni hisoblang.
vektorini 1 2 3 , , а а а bazis orqali yoying
1 2 3 2, 3,2 ,
1,2,1 , 4,1,2 ,
1,2,2 . а а а b
2 1 1 1 3 2 2 3 5 1 1 2 2 1 1 3
A matrisarangi 6dan nechtakam Agar 4 0 1 3 2 1 A
va 2 0 1 2 3 1 B
matritsalar berilgan bo`lsa, T T B A ni hisoblang.
vektorini 1 2 3 , , а а а bazis orqali yoying
1 2 3 1, 3,1 ,
3,2,1 , 2,1,2 ,
1,2,3 . а а а b
Tenglamalarsistemasinite kshiring: . 5 4 2 3 , 8 2 4 7 , 2 3 2 3 2 1 3 2 1 3 2 1
x x x x x x x x
Agar 4 0 1 3 2 1 A
va 2 0 1 2 3 1 B
matritsalar berilgan bo`lsa,
A B ni hisoblang. b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 2, 3,1 , 1,2,1 ,
2,1,2 , 1,2,3 .
а а а b
Sistemani yeching
. 20 4 3 , 5 4 3 , 13 3 2 , 12 3 2 1 3 2 3 2 1 3 2 1 x x x x x x x x x x x
Agar 4 3 2
va
1 3 2
matritsalar berilgan bo`lsa,
ni hisoblang. b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 1,3, 2 ,
2,3, 2 , 1, 1,2 ,
2, 1,2 . а а а b
Tenglamalar sistemani nechtayechimgaega
. 8 5 7 3 , 7 5 3 2 , 1 2 4 4 3 2 1 4 3 2 1 3 2 1
x x x x x x x x x x
Agar 4 3 2
va
1 3 2
matritsalar berilgan bo`lsa,
ni hisoblang.
vektorini 1 2 3 , , а а а bazis orqali yoying
1 2 3 3,2, 2 , 2,1, 2 , 1, 1,2 ,
2, 1,2 . а а а b
Sistemani yeching 1 2 3 4 2 3 4 1 2 4 1 2 3 4 2 2 2, 2 7, 2 2 7, 2 2 1.
x x x x x x x x x x x x x
Agar 4 2 3 5 1 2
va
2 3 4 B
matritsalar berilgan bo`lsa,
B A ni hisoblang. b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 1,2, 3 ,
1,3, 4 , 2,0,5 ,
2, 1,1 . а а а b Tenglamalar sistemasini yeching
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 3 5 4 2 9, 5 3 2 7 11,
7 4 5 3 2, 4 2 3 4 15. x x x x x x x x x x x x x x x x
Agar 4 2 3 5 1 2
va b vektorini 1 2 3 , , а а а bazis orqali yoying Tenglamalar sistemanitekshiring 2 3 4 B
matritsalar berilgan bo`lsa, T T A B ni hisoblang. 1 2 3 1, 2, 3 , 1,2, 4 , 2,1,3 ,
1, 2,3 . а а а b
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2 1, 3 2 2 3 2, 5 2 1, 2 3 4. x x x x x x x x x x x x x x x x
1 0 0 4 1 0 3 2 1
matritsa LDU A yoyilmaning qaysi matritsasi bo`la oladi?
vektorini 1 2 3 , , а а а bazis orqali yoying
1 2 3 2, 2, 3 , 1,2,1 , 2,4,3 ,
1, 2,3 . а а а b
Tenglamalar sistemani nechtayechimgaega 1 2
4 1 2 3 1 2 3 4 1 2 3 4 2 4 0, 3 1, 3 7 2 5, 3 4 5. x x x x x x x x x x x x x x x
4 1 3 0 3 2 0 0 1 matritsa LDU A yoyilmaning qaysi matritsasi bo`la oladi?
vektorini 1 2 3 , , а а а bazis orqali yoying
1 2 3 1, 2,3 , 1, 2,1 , 2, 4,3 ,
1, 2,3 . а а а b
2 4 3 1 0 1 2 1 4 2 0 1 1 3 1 4 7 4 4 5 A ( ) rang A ni hisoblang
1 4 3 0 1 2 0 0 1
matritsa LDU A yoyilmaning qaysi matritsasi bo`la oladi? b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 2, 2,3 ,
3,2, 4 , 2, 2,3 ,
2, 2,3 . а а а b
2 4 3 1 0 1 2 1 4 2 0 1 1 3 1 4 7 4 4 5
( ) T rang A ni
Agar 4 0 1 3 2 1
va
2 0 1 2 3 1 B
matritsalar berilgan bo`lsa, T T A B ni hisoblang. b vektorini 1 2
, ,
bazis orqali yoying
1 2 3 3, 4,2 , 5,3, 1 ,
3, 1,2 , 1, 3,2 .
а а а b
Tenglamalarsistemasiyechimga egami? 1 2 3 4 1 2 3 4 1 2 3 4 5 2 7, 2 4 2 1, 3 6 5 0. x x x x x x x x x x x x
Quyidagilardan qaysi biri A kvadrat
matritsaning LDU A yoyilmasidagi D matritsa bo`la oladi? To'rt o’lchamli fazoda basis tashkil qiladimi:
1;2;3;4 , 2;5;6;8 , 1;3;2;4 , 2;5;4;7 .
Tenglamalarsistemasinechtayec himgaega? 1 2
2 1 2 7 3 2, 2 3, 4 9 11.
x x x x x x
Agar k n o`lchamli A matritsa va m p o`lchamli To'rt o’lchamli fazoda basis tashkil qiladimi: Sistemani yeching
B matritsalar uchun B A
ko`paytma mavjud bo`lsa, quyidagi tenglik o`rinli:
3; 2;1 , 2;1;2 , 3; 1; 2 , 0;1;2 .
1 2 1 2 1 2 7 3 2, 2 3, 4 9 11. x x x x x x
Agar k n o`lchamli A matritsa va m p o`lchamli B matritsalar uchun A B
ko`paytma mavjud bo`lsa, quyidagi tenglik o`rinli: Berilgan vektorlar sistemasi bazis tashkil qiladimi:
1;2; 1; 2 , 0;2;1; 3 , 1;0;0;5 .
Ushbu
{ 𝑥 1 + 𝑥 2 − 3𝑥 3 = −1
2𝑥 1 + 𝑥 2 − 2𝑥
3 = 1
𝑥 1 + 𝑥 2 + 𝑥
3 = 3
𝑥 1 + 2𝑥 2 − 3𝑥
3 = 1
sistеma birgalikdami?
Quyidagilardan qaysi biri A kvadrat matritsaning LDU A yoyilmasidagi U matritsa bo`la oladi?
Vektorlar sistemasi chiziqli bog’liqmi: 1 2 2 1 ,
1 , 0 3 4 2
Ushbu { 𝑥 1 − 2𝑥
2 + 𝑥
3 + 𝑥
4 = 1,
𝑥 1 − 2𝑥 2 + 𝑥
3 − 𝑥
4 = −1,
𝑥 1 − 2𝑥 2 + 𝑥
3 + 5𝑥
4 = 5
sistеma birgalikdami? Agar
4 0 1 3 2 1
va
2 0 1 2 3 1 B matritsalar berilgan bo`lsa, ) det( B A ni hisoblang
Vektorlar sistemasi chiziqli bog’liqmi: 1 2 1 2 1 3 1 ,
3 , 1 1 1 1 2 3 1
а а
1 2 1 3 3 1 0 7 2 3 1 4 A ( ) T rang A ni hisoblang
Agar
0 2 1 3 1 2 A
va 1 5 4 2 0 3
matritsalar berilgan bo`lsa,
A det ni hisoblang Berilgan vektorlar sistemasi bazis tashkil qiladimi:
4; 2;2; , 3;3; 4 ,
2; 4;3 . а b c
1 3 2 2 1 3 1 0 1 3 7 4
A
( ) rang A ni hisoblang
Agar 0 3 2 1 1 2 A 1 4 0 5 2 3
va
matritsalar berilgan bo`lsa, A B det ni hisoblang
Berilgan vektorlar sistemasi bazis tashkil qiladimi: 4;1;4 ,
2; 1;1 , 3;1;5 .
а b c
2 1 0 1 1 2 3 2 1 6 4 2 B ( ) rang B ni hisoblang
Berilgan 7 4 6 2 A
matritsani LU ko`paytmaga yoying
Berilgan vektorlar sistemasi bazis tashkil qiladimi: 1; 2;3 ,
4;7;2 , 6;4;2 .
а b c
Ushbu { 𝑥 1 + 𝑥
2 − 𝑥
3 = 4,
2𝑥 1 + 4𝑥 2 + 𝑥
3 = 9,
𝑥 1 − 𝑥 2 + 𝑥
3 = −2
2𝑥 1 + 5𝑥 2 − 3𝑥
3 = 15
tenglamalarsistеmabirgalikdami ?
7 4 6 2 A
matritsani LDU ko`paytmaga yoying
Vektorlar sistemasi chiziqli bog’liqmi: 1;2;4 ,
2; 1;0 , 4;3; 8 .
а b c
Ushbutenglamalarsistemasiniye ching
{ 𝑥 1 + 𝑥 2 − 𝑥 3 = 4,
2𝑥 1 + 4𝑥 2 + 𝑥
3 = 9,
𝑥 1 − 𝑥 2 + 𝑥
3 = −2
2𝑥 1 + 5𝑥 2 − 3𝑥
3 = 15
Agar 4 3 2
va
1 3 2
matritsalar berilgan bo`lsa,
A det ni hisoblang. , ,
va shu basis asosida d vektorning koordinatalarini toping: 2;0;1 , 1;2; 1 ,
0;4; 1 , 1; 2;3 .
а b c d
Tenglamalar sistemasi yechimlari yig‘indisini toping
0 3 2 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x .
Agar
2 1 2
va
1 3 4
matritsalar berilgan bo`lsa,
A det ni hisoblang. , ,
va shu basis asosida d vektorning koordinatalarini toping: Tenglamalar sistemasi yechimlari ko’paytmasini toping
0 3 2 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x .
1;2;3 , 2;3;7 , 1;3;1 ,
2;3;4 . а b c d
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?
, ,
а b c vektorlar bazis tashkil qiladi va shu basis asosida d vektorning koordinatalarini toping: 1;2;3 , 2; 2;1 ,
1; 2;0 , 0;3;1 .
а b c d
Tenglamalar sistemasi yechimlari yig‘indisi 12 danqanchakam? 0 3 2 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x .
Agar
7 2 4 1 A matritsa berilgan bo`lsa,
I A/ matritsani tuzing va Gauss- Jordan usulida
B I /
matritsaga keltiring(I-birlik matritsa)
, , а b c vektorlar bazis tashkil qiladi va shu basis asosida d vektorning koordinatalarini toping: 5;1;2 , 3;4; 1 ,
4;2;1 , 3;5;4 .
а b c d
Tenglamlar sistemani yeching 1 2
1 2 3 1 2 3 1 3 2 7 13 0, 3 14 12 18, 5 25 16 39,
14 18.
x x x x x x x x x x x
.
Agar
4 3 3 2 A matritsa berilgan bo`lsa,
matritsani tuzing va Gauss- Jordan usulida
matritsaga keltiring(I-birlik matritsa)
Tenglamalar sistemasini hisoblang 1 2 3 1 2 3 1 2 3 2 0 2 0 4 3 0
x x x x x x x x
Tenglamalarsistemani tekshiring 1 2 3 1 2 3 1 2 3 2 3 1, 3 2 3, 2 2. x x x x x x x x x
Agar 3 4 2 3
matritsa berilgan bo`lsa,
matritsani tuzing va Gauss- Jordan usulida
B I /
matritsaga keltiring(I-birlik matritsa) Sistemaning umumiy yechimini toping 1 2 3 4 1 2 3 4 1 2 3 4 3 2 0 0 6 4 2 0 x x x x x x x x x x x x Tenglamalarsistemani tekshiring 1 2 3 4 1 2 3 4 1 2 3 4 3 3 14 1, 6 2 3 4, 9 3 5 6 5.
x x x x x x x x x x x
Agar 3 1 2 A
va 1 3 4 B
matritsalar berilgan bo`lsa, B A det ni hisoblang. Tenglamalar sistemasini hisoblang
1 2 3 1 2 3 1 2 3 3 2 0 2 3 0 3 4 0
x x x x x x x x
Tenglamalar sistemani yeching: 1 2
1 2 3 1 2 1 2 3 1 3 3 6, 5 12,
2 4 6, 2 3 3, 5 4 3. x x x x x x x x x x x x x
1 6 4 6 1 3 0 1 1 A
matritsaning LU ko`paytma shaklidagi U matritsani aniqlang Tenglamalar sistemasini hisoblang
1
3 1 2 3 1 2 3 3 2 0 2 3 0 0
x x x x x x x x
Tenglamalar sistemani tekshiring 1 2 3 4 1 2 3 4 1 2 3 4 2 3 4 7, 2 4 5 2, 5 10 7 6 11.
x x x x x x x x x x x x 3 7 4 6 0 6 4 1 2 A
matritsaning LU ko`paytma shaklidagi U matritsani aniqlang
Tenglamalar sistemasini hisoblang
1
3 1 2 3 2 5 2 0 4 3 0
x x x x x
Tenglamalar sistemani tekshiring 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2 3 4 1, 2 2 2, 4 3 5 2 4, 7 4 7 5 7. x x x x x x x x x x x x x x x x
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?
Tenglamalar sistemasini hisoblang 1 2 3 1 2 3 3 2 2 0 5 2 3 0 x x x x x x
Sistemani yeching: 1 2 3 1 2 3 1 2 3 2 3 2 9, 2 3 14,
3 4 16. x x x x x x x x x
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?
Tenglamalar sistemasini hisoblang 1 2 3 1 2 3 3 2 0 2 3 5 0 0 x x x x x x x y z
Tenglamalar sistemasi yechimlari yig‘indisi 10
danqanchakam? 1 2 3 1 2 3 1 2 3 6, 2 3, 0.
x x x x x x x x
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 Tenglamalar sistemasini hisoblang 1 2
1 2 3 2 3 0 2 5 0 3 2 0 x x x x x x x y z
Tenglamalarsistemani tekshiring
biri noo`rin? 1 2 3 1 2 3 1 2 3 2 3 2, 7 4 2 8, 3 2 4 5. x x x x x x x x x 2 4 1 2 7 2 1 3 1 A matritsaning LU ko`paytma shaklidagi L matritsani aniqlang Tenglamalar sistemasini hisoblang 1 2 3 1 2 3 1 2 3 5 0 3 2 13 0 2 8 0 x x x x x x x x x
Tenglamalar sistemani tekshiring: 1 2
1 2 3 1 2 3 2 3 2, 7 4 2 8, 3 2 4 5.
x x x x x x x x
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).
Tenglamalar sistemasini hisoblang 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2 3 0 2 3 2 0 4 3 0 3 5 2 0 x x x x x x x x x x x x x x x x
Tenglamalar sistemani tekshiring: 1 2 3 1 2 3 2 3 1 2 3 12, 2 3 13, 3 4 5, 3 4 20. x x x x x x x x x x x
Berilgan 2 4 1 2 7 2 1 3 1
matritsani LU ko`paytmaga yoying Tenglamalar sistemasini hisoblang 1 4
1 2 4 4 3 2 0 3 0 0 x x x x x x x x
Tenglamalar sistemani yeching: 1 2
1 2 3 2 3 1 2 3 12, 2 3 13, 3 4 5, 3 4 20. x x x x x x x x x x x
Berilgan 1 3 3 6 5 2 2 4 1 A
matritsani LU ko`paytmaga yoying
Tenglamalar sistemasini hisoblang 1 2 1 2 3 2 3 0 0 0 x x x x x x x
Tenglamalar sistemani tekshiring 1 2 3 1 2 3 4 1 2 3 4 4 2 1, 2 3 5 7, 3 7 5 8.
x x x x x x x x x x
Berilgan 3 7 4 6 0 6 4 1 2 A
matritsani LU ko`paytmaga yoying.
Tenglamalar sistemasini hisoblang 1 2 3 4 1 2 3 1 3 4 2 3 4 0 2 0 2 3 0 2 0 x x x x x x x x x x x x x
Tenglamalar sistemani tekshiring 1 2 3 1 2 3 4 1 2 3 4 4 2 1, 2 3 5 7, 3 7 5 8.
x x x x x x x x x x
1 6 4 6 1 3 0 1 1
Tenglamalar sistemasini fundamental yechimini toping Tenglamalar sistemani tekshiring
matritsaning LU ko`paytma shaklidagi L matritsani aniqlang.
1
3 4 1 2 3 4 1 2 3 4 1 2 3 4 2 4 3 0 3 5 6 4 0 4 5 2 3 0 3 8 24 19 0 x x x x x x x x x x x x x x x x 1 2 3 1 2 3 4 1 2 3 4 4 2 1, 2 3 5 7, 3 7 5 8.
x x x x x x x x x x
3 7 4 6 0 6 4 1 2 A
matritsaning LU ko`paytma shaklidagi L matritsani aniqlang
Tenglamalar sistemasini fundamental yechimini toping. 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 2 0 3 6 5 4 3 0 2 7 4 3 0 2 4 2 3 3 0 x x x x x x x x x x x x x x x x x x x x
Tenglamalar sistemani yeching 1 2 3 4 2 3 4 1 2 2 5, 3, 2.
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