1. Determinantni hisoblang

Variant 20
1. Determinantni hisoblang:
a) → = 2×4×4 + (-1)×(-2)×3 + (-1)×3×(-2) - 3×4×(-1) – (-2)×(-2)×2 – 4×3×(-1) = 60
b) A₁₁=4 =8; A₁₂=-2× =0; A₁₃= =0; A₁₄= - =-6
A₁₁ + A₁₂ + A₁₃ + A₁₄ = 8 + 0 + 0 – 6 = 2
c) → A₁₁= =69; A₁₂=-2× =34; A₁₃=4× =-84; A₁₄=-7 =-77
A₁₁ + A₁₂ + A₁₃ + A₁₄ = 69 + 34 – 84 -77= -58
2. Berilgan matritsalar
A= va B= yordamida quyidagilarni toping:
a) 5A – 2B → - =
b) AB – BA → - = - = =
c) A^-1= = 3; A₁₁=0; A₁₂=-6; A₁₃=3; A₂₁=1; A₂₂=0; A₂₃=0; A₃₁=-1; A₃₂=15; A₃₃=-6
Agebraik to’ldiruvchilardan matritsa yasaymiz: endi buni transponerlaymiz:
Bu matritsaga dastlabki matritsaning determinantini teskari ko’paytiramiz: 1/3× =
3. Matritsali tenglamani ishlang.
a) × X = → X= ^-1 × = × =
b) ×X× = → X= ^-1× ^-1× =

4. f(x)=2x²-3x+4 f(A) ni toping agar A=

2× × - 3× + 4× = - + =
5. Matritsalarni ko’paytiring:
C= ; D= ; K=
Matritsalarni bir-biriga ko’paytirish uchun birinchi matritsa ustunlar souni ikkinchi matritsa satrlar soniga teng bo’lishi kerak. Shunda, birinchi matritsaning mos satr elementlarini ikkinchi matritsaning mos ustun elementlariga ko’paytirib qo’shib qoyish kifoya. Yuqoridagi matritsalardan, C×B, D×K va K×D larni toppish mumkin.
C×B= =
D×K= =
K×D= =
6. Tenglamalar sistemasini Kramer usulida yeching.
a) → = ∆=6
= ∆₁=12

=∆₂=6

=∆₃=6 x₁=∆₁/∆=2; x₂=1; x₃=1;

b) → =∆=35

= ∆₁=70
=∆₂=749
=∆₃=490
=∆₄=-168 x₁=∆₁/∆=2; x₂=21.4; x₃=14; x₄=-4.8

7. Tenglamalar sistemasini teskari matritsa usulida yeching: Ax=B

a) → X= B= X=A^-1×B
A^-1= = 1; A₁₁=-3; A₁₂=0; A₁₃=-4; A₂₁=2; A₂₂=1; A₂₃=3; A₃₁=-3; A₃₂=-2; A₃₃=-5
Agebraik to’ldiruvchilardan matritsa yasaymiz: endi buni transponerlaymiz:
Bu matritsaga dastlabki matritsaning determinantini teskari ko’paytirishimiz kerak, lekin bu matritsada determinant 1 bo’lgani uchun bu qadam shart emas.
X=A^-1×B= × = x₁=-8; x₂=-4; x₃=-13;
b) → X= B= X=A^-1×B
A^-1= = -1; A₁₁=-3; A₁₂=0; A₁₃=-4; A₂₁=2; A₂₂=1; A₂₃=3; A₃₁=3; A₃₂=2; A₃₃=5
Agebraik to’ldiruvchilardan matritsa yasaymiz: endi buni transponerlaymiz:
Bu matritsaga dastlabki matritsaning determinantini teskari ko’paytirishimiz kerak, determinant -1 bo’lgani uchun matritsa elementlarining ishoralarini almashtirish kifoya
X=A^-1×B= × = x₁=1; x₂=3; x₃=3;
8. Tenglamalar sistemasini Gauss usulida yeching.
→ x₁=1; x₂=2; x₃=-2;
b) → x₁=-8; x₂=b; x₃=2b; x₄=b-3
(9-mashq, 10-mashqlarni harakat qildim, yecholmadim)