Mustakil ta’lim mavzulari Dars soatlari hajmi

1. 
   

   №	Mustakil ta’lim mavzulari	Dars soatlari hajmi
   1	Determinantlar.	2
   2	Teskari matrista.	2
   3	Chizikli tenglamalar sistemasini matristaviy usul,	2
   4	Kramer koidasi va Gauss usulida echish.	2
   5	Kompleks sonlar	2
   6	Ko’p tarmokli iqtisod uchun balans modeli.	2
   7	Chizikli fazo va uning elementlari	4
   8	Chizikli almashtirish matristasi	4
   9	Chizikli operatorlar. Evklid fazosi	4
   10	Kvadratik formalar.	4
   11	Almashtirishning chizikli modeli	4
   12	To’k’ri chizik tenglamalari va unga doir asosiy masalalar	4
   13	Vektorlarning skalyar, vektor va aralash ko’paytmalari .Vektorlarning skalyar, vektor va aralash ko’paytmalari.	4
   14	Fazoda tekislik va to’k’ri chizik tenglamalari	4

   namunaviy hisob topshiriklari
   

1. berilgan determinantni uch usul bilan hisoblang:

a) uni i-satr elementlari bo’yicha yoyib;

b) uni j-ustun elementlari bo’yicha yoyib;

c) oldin j-ustundagi bittadan boshka elementlarni nolga aylantirib, so’ngra shu ustun elementlari bo’yicha yoyib.

1.1 1.2 1.3

i=2, j=4 i=4, j=3 i=3, j=3

1.4 1.5 1.6

i=1, j=2 i=3, j=2 i=2, j=3

1.7 1.8 1.9

i=4, j=1 i=2, j=2 i=1, j=3

1.10 1.11 1.12

i=4, j=4 i=4, j=2 i=1, j=4

1.13 1.14 1.15

i=1, j=1 i=3, j=1 i=3, j=4

1.16 1.17 1.18

i=2, j=1 i=3, j=1 i=2, j=2

1.19 1.20 1.21

i=2, j=3 i=4, j=4 i=1, j=2

1.22 1.23 1.24

i=3, j=3 i=4, j=2 i=3, j=4

1.25 1.26 1.27

i=3, j=2 i=1, j=4 i=4, j=3

1.28 1.29 1.30

i=2, j=4 i=1, j=3 i=4, j=1

2. A va B matritsalar berilgan:

a) AB va BA ko’paytmalarni toping;

b) A^-1 ni toping va AA^-1=A^-1A=E ekanligini tekshiring:

2.1 A= B=

2.2 A= B=

2.3 A= B=

2.4 A= B=

2.5 A= B=

2.6 A= B=

2.7 A= B=

2.8 A= B=

2.9 A= B=

2.10 A= B=

2.11 A= B=

2.12 A= B=

2.13 A= B=

2.14 A= B=

2.15 A= B=

2.16 A= B=

2.17 A= B=

2.18 A= B=

2.19 A= B=

2.20 A= B=

2.21 A= B=

2.22 A= B=

2.23 A= B=

2.24 A= B=

2.25 A= B=

2.26 A= B=

2.27 A= B=

2.28 A= B=

2.29 A= B=

2.30 A= B=

3. Berilgan tenglamalar sistemasining birgalikda ekanligini tekshiring, agar birgalikda bo’lsa ularni:

a) Kramer koidasidan foydalanib;

b) Matritsa usuli;
c) Gauss usuli bilan yeching:

1. 
   a) b)
   

3.2 a) b)

3.3 a) b)

3.4 a) b)

3.5 a) b)

3.6 a) b)

3.7 a) b)

3.8 a) b)

3.9 a) b)

3.10 a) b)

3.11 a) b)

3.12 a) b)

3.13 a) b)

3.14 a) b)

3.15 a) b)

3.16 a) b)

3.17 a) b)

3.18 a) b)

3.19 a) b)

3.20 a) b)

3.21 a) b)

3.22 a) b)

3.23 a) b)

3.24 a) b)

3.25 a) b)

3.26 a) b)

3.27 a) b)

3.28 a) b)

3.29 a) b)

3.30 a) b)

4. Bir jinsli chizikli tenglamalar sistemalarini yeching:

4.1 a) b)

4.2 a) b)

4.3 a) b)

4.4 a) b)

4.5 a) b)

4.6 a) b)

4.7 a) b)

4.8 a) b)

4.9 a) b)

4.10 a) b)

4.11 a) b)

4.12 a) b)

4.13 a) b)

4.14 a) b)

4.15 a) b)

4.16 a) b)

4.17 a) b)

4.18 a) b)

4.19 a) b)

4.20 a) b)

4.21 a) b)

4.22 a) b)

4.23 a) b)

4.24 a) b)

4.25 a) b)

4.26 a) b)

4.27 a) b)

4.28 a) b)

4.29 a) b)

4.30 a) b)

2-namunaviy hisob topshiriklari

1. ABC uchburchkning uchlari berilgan. Kuyidagilarni toping:

a) AB yon tamon tenglamasini;

b) C uchidan AB tomonga tushirilgan balandlik tenglamasini;

c) A uchidan BC tomonga tushirilgan mediana tenglamasini;

d) va bandlarda topilgan balandlik bilan mediananing kesishgan nuktasini;

e) C nuktadan o’tuvchi AB tomonga parallel to’g’ri chizik tenglamasini;

f) C nuktadan AB tomongacha bo’lgan masofani.

1.1 A(4,-5) B(6, 9) C(-4, -1)

1.2 A(1, -3) B(-5, 4) C(-2, 10)

1.3 A(1, 8) B(-5, -4) C(-1, -3)

1.4 A(0, 4) B(5, -3) C(-6, -2)

1.5 A(6, -4) B(-8, 3) C(-2, -7)

1.6 A(2, 3) B(-4, -7) C(2, 0)

1.7 A(-4, -8) B(4, 1) C(0, 7)

1.8 A(4, -2) B(7, 0) C(-3, 1)

1.9 A(4, 1) B(-2, 8) C(1, -5)

1.10 A(4, 0) B(1, -3) C(5, 2)

1.11 A(7, 10) B(1, 3) C(4, -2)

1.12 A(8, 6) B(1, 3) C(-2, -3)

1.13 A(11, -3) B(-1, -3) C(7, 1)

1.14 A(5, 9) B(4, -1) C(0, 1)

1.15 A(7, 3) B(1, 7) C(-2, 1 )

1.16 A(1, 6) B(6, 1) C(-3, -2)

1.17 A(2, 6) B(6, -6) C(2, -4)

1.18 A(10, 1) B(3, 7) C(-3, 4)

1.19 A(8, 3) B(2, 8) C(-4, 4)

1.20 A(7, 7) B(-7, 5) C(-3, -3)

1.21 A(3, -3) B(4, 3) C(-6, 1)

1.22 A(6, 2) B(-6, 8) C(2, -4)

1.23 A(7, 5) B(-4, 0) C(2, -5)

1.24 A(8, -1) B(2, 6) C(-4, 4)

1.25 A(-5, 0) B(2, -6) C(8, -3)

1.26 A(1, -4) B(-1, 10) C(-9, 6)

1.27 A(-3, 7) B(-1, 3) C(2, -4)

1.28 A(10, 4) B(-4, 6) C(-1, 3)

1.29 A(2, -6) B(3, 11) C(-1, 3)

1.30 A(-5, 5) B(4, -7) C(-2, -7)

2. ABCD piramidaning uchlari berilgan. Kuyidagilarni toping:

a) ABC tekislik tenglamasini;

b) AB kirra tenglamasini;

c) D uchidan o’tuvchi ABC o’kka perpendikulyar to’g’ri chizik tenglamasini;

d) C uchidan o’tuvchi AB kirraga parallel to’g’ri chizik tenglamasini;

e) D uchidan o’tuvchi AB kirraga perpendikulyar tekislik tenglamasini;

f) AD kirra bilan ABC yok orasidagi burchak kosinusini;

g) ABC va ABD yoklar orasidagi burchak kosinusini;

h) D uchidan ABC yokkacha bo’lgan masofani.

2.1 A(7, 3, 5) B(5, 3, 2) C(10, 2, 4) D(7, -2, 1)

2.2 A(-8, -6, -3) B(4, 2, 1) C(0, 5, 2) D(0, 2, 5)

2.3 A(7, -3, 14) B(-6, 0, 5) C(1, 2, 1) D(-2, -1, 2)

2.4 A(5, 5, -6) B(-4, -8, 4) C(1, 7, -1) D(-4, 0, -2)

2.5 A(7, -8, -1) B(-3, -6, -2) C(2, -3, -5) D(5, 4, 14)

2.6 A(16, -8, -13) B(6, 2, 5) C(-3, 0, 3) D(0, 2, 1)

2.7 A(7, 3, -5) B(1, 2, 3) C(-1, 2, 1) D(2, -1, 2)

2.8 A(8, 3, 2) B(4, -2, 2) C(3, 1, -1) D(2, 1, 1)

2.9 A(8, -4, -5) B(7, 3, 6) C(-2, 1, 4) D(1, 3, 2)

2.10 A(6, -7, -3) B(1, 2, 3) C(1, 3, 2) D(2, 1, 1)

2.11 A(-12, 7, -1) B(0, -2, -5) C(-4, 5, 1) D(-7, 4, -3)

2.12 A(-5, -6, 1) B(-2, 1, 2) C(0,-1, 4) D(-3, 2, -1)

2.13 A(-1, 0, -7) B(4, -5, 3) C(-2, 1, -9) D(1, -1, -3)

2.14 A(2, 4, -2) B(-1, 1, 2) C(3, 0, -2) D(1, -1, 1)

2.15 A(4, -1, 2) B(-1, 1, 0) C(2, -1, 1) D(0, 2, 1)

2.16 A(16, -9, -5) B(1, -2, 2) C(-1, 2, 1) D(2, 0, 1)

2.17 A(-9, -2, 3) B(6, -1, -2) C(1, 0, 1) D(-3, 2, 1)

2.18 A(-10, 7, -6) B-3, 0, -6) C(-5, 3, -2) D(-1, 10, 3)

2.19 A(5, 3, -2) B(-1, 0, 3) C(-4, -2, -1) D(4, 2, -1)

2.20 A(-5, 4, -3) B(5, -1, 2) C(2, 1, -4) D(1, -3, 0)

2.21 A(0, 3, 4) B(1, 0, 3) C(2, -1, 4) D(0, 3, 1)

2.22 A(-16, 20, -21) B(-4, 1, 3) C(2, 3, 0) D(-1, -1, -2)

2.23 A(2, -1, 1) B(3, 7, -2) C(3, 6, -3) D(-7, 5, 1)

2.24 A(8, -10, 2) B(-3, 3, -1) C(0, -6, 5) D(-3, -4, 2)

2.25 A(7, 2, -3) B(4, 1, 1) C(2, 1, 2) D(2, -1, 1)

2.26 A(5, -4, 5) B(1, 0, -1) C(1, 2, 2) D(6, 3, 1)

2.27 A(8, 1, -12) B(8, 5, -10) C(0, -3, 2) D(6, 2, -4)

2.28 A(8, 1, 10) B(-1, -2, -5) C(-2, -1, 7) D(4, 2, 7)

2.29 A(8, 1, -3) B(2, -3, -7) C(-2, 5, 3) D(4, 1, 2)

2.30 A(-7, -8, 10) B(-3, 6, 3) C(-3, 0, -6) D(2, -5, -1)

3. To’g’ri chizikning kanonik tenglamasini yozing.

3.1 3.2 3.3

3.4 3.5 3.6

3.7 3.8 3.9

3.10 3.11 3.12

3.13 3.14 3.15

3.16 3.17 3.18

3.19 3.20 3.21

3.22 3.23 3.24

3.25 3.26 3.27

3.28 3.29 3.30

4. Berilgan to’g’ri chizik bilan tekislikning kesisish nuktasini toping.

4.1 x+2y-2z+25=0

4.2 2x-7y-3z-21=0

4.3 5x-2y-z-13=0

4.4 4-y+3z+6=0

4.5 5x-2y+3z-3=0

4.6 5x-2y+3z-3=0

4.7 4x+9y+5z=0

4.8 6x-y-4z-3=0

4.9 5x-7y-3z+11=0

4.10 3x+7y+z+11=0

4.11 3x-2y-z-6=0

4.12 4x-5y+2z+24=0

4.13 7x+4y+3z-16=0

4.14 3x+4y-5z+20=0

4.15 7x-3y+2z-28=0

4.16 4x+y-7z-19=0

4.17 5x-3y+z-36=0

4.18 4x-y+5z+3=0

4.19 x-2y-z+2=0

4.20 4x+2y-3z+8=0

4.21 x-2y-4z+11=0

4.22 5x+3y-2z+7=0

4.23 3x-y+2z+23=0

4.24 4x-2y+z-19=0

4.25 3x-2y+z-8=0

4.26 5x+2y+z-15=0

4.27 7x+3y+z-25=0

4.28 4x-y+2z=0

4.29 5x-y-3z+10=0

4.30 x+3y-5z-21=0