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Quyidagi matrisalarning rangini toping
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oliy matematika
- Bu sahifa navigatsiya:
- 4,5-mashg’ulotlar. Chiziqli tenglamalar sistemasi Mustaqil bajarish uchun topshiriqlar
- Quyidagi tenglamalar sistemasi yechilsin
- 6- mashg’ulot. Tekislikda analitik geometriya 1 . Tekislikda analitik geometriyaning sodda masalalari mavzusibo’yicha mu sta qil bajarish uchun m asalalar
- 7-mashg’ulot . To’g’ri chiziq va uning tenglamalari m avzusibo’yicha mustaqil bajarish uchun masalalar
Quyidagi matrisalarning rangini toping 1. 1 4 1 5 7 7 0 5 3 1 4 3 2 3 5 5 2 3 1 3 2. 48 20 32 25 134 54 94 75 132 53 94 75 43 17 31 25 3. 0 20 10 17 23 1 5 2 61 3 4 1 30 4 7 1 11 7 1 3 12 10 5 5 . 6 2 2 1 3 6 3 0 2 2 1 2 4 . 5 0 5 10 1 2 3 8 2 8 5 1 1 4 3 1 . 4 2 4 6 7 1 1 3 1 2 3 0 2 4 3 5 . 9 7 7 4 0 1 1 0 2 4 3 2 1 . 8 0 1 5 4 1 6 5 8 5 1 2 2 1 3 1 . 7 62 0 4 1 3 1 2 3 1 4 2 4 2 1 5 3 . 12 0 1 5 4 1 6 5 8 5 2 2 2 1 3 1 . 11 0 6 6 8 1 1 4 1 1 2 3 6 3 5 7 . 10 4 3 5 1 4 2 1 1 3 2 1 2 3 1 1 . 15 2 4 6 7 1 1 3 1 2 3 0 2 4 3 5 . 14 2 0 2 5 1 2 1 1 0 4 4 3 . 13 4,5-mashg’ulotlar. Chiziqli tenglamalar sistemasi Mustaqil bajarish uchun topshiriqlar Determinantlar yordamida quyidagi tenglamalar sistemasini yeching: 1) 40 5 4 7 2 3 y x y x 2) 2 2 1 3 y ax y ax 3) 8 4 7 4 2 5 y x y x Quyidagi tenglamalar sistemasi yechilsin: 4) 0 4 3 4 0 5 4 5 0 2 3 2 z y x z y x z y x 5) 2 5 3 3 4 2 1 3 4 2 z y x z y x z y x 6) 0 3 4 0 2 5 2 z y x z y x 7) 0 4 3 0 3 2 0 2 3 z y x z y x z y x 8) 0 0 3 2 0 2 3 z y x z y x z y x 9) 1 3 3 6 4 2 4 3 2 z y x z y x z y x 10) 7 2 3 3 3 2 4 3 2 z y x z y x z y x 11) 10 2 3 3 3 2 4 3 22 z y x z y x z y x Berilgan tenglamalar sistemasining birgalikda ekanligini tekshiring, agar birgalikda bo’lsa, ularni: a) Kramer qoidasidan foydalanib, b) Matrisa usuli, c) Gauss usuli bilan yeching: 1) 11 4 2 3 11 2 4 3 4 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 2) 9 4 6 3 12 5 6 2 17 3 6 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 3) 3 3 4 2 6 3 8 1 3 2 1 3 2 1 3 2 1 x x x x x x x x x 4) 8 2 3 2 2 3 3 3 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 5) 6 5 2 3 20 4 3 2 6 3 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 6) 8 2 3 3 8 3 5 2 9 3 2 1 3 2 1 3 2 1 x x x x x x x x x 63 7. 2 4 4 4 2 2 1 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 8. 8 3 2 4 17 4 5 3 5 3 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 9. ; 7 6 5 3 , 5 3 , 7 2 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 10. 6 7 1 2 3 4 2 3 3 1 3 2 1 3 2 1 x x x x x x x x 11. ; 3 2 4 3 , 0 3 4 2 , 2 5 3 2 1 3 2 1 3 2 1 x x x x x x x x x 12. 8 2 4 4 3 3 5 2 5 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 13. 12 5 3 21 13 2 5 10 5 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 14. 7 5 5 3 7 3 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 15. 13 3 4 2 1 5 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 16. 5 3 2 3 2 2 2 2 3 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 17 1 2 14 3 5 3 10 7 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 18. 7 4 3 2 3 7 3 7 4 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x 19. 10 4 3 2 0 3 2 14 5 2 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 20. ; 15 2 3 4 , 1 3 5 2 , 9 2 6 5 3 2 1 3 2 1 3 2 1 x x x x x x x x x 10) 7 2 3 3 3 2 4 3 2 z y x z y x z y x 11) 10 2 3 3 3 2 4 3 22 z y x z y x z y x Berilgan tenglamalar sistemasining birgalikda ekanligini tekshiring, agar birgalikda bo’lsa, ularni: d) Kramer qoidasidan foydalanib, e) Matrisa usuli, f) Gauss usuli bilan yeching: 1) 11 4 2 3 11 2 4 3 4 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 2) 9 4 6 3 12 5 6 2 17 3 6 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 3) 3 3 4 2 6 3 8 1 3 2 1 3 2 1 3 2 1 x x x x x x x x x 4) 8 2 3 2 2 3 3 3 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 5) 6 5 2 3 20 4 3 2 6 3 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 6) 8 2 3 3 8 3 5 2 9 3 2 1 3 2 1 3 2 1 x x x x x x x x x 7. 2 4 4 4 2 2 1 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 8. 8 3 2 4 17 4 5 3 5 3 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 64 9. ; 7 6 5 3 , 5 3 , 7 2 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 10. 6 7 1 2 3 4 2 3 3 1 3 2 1 3 2 1 x x x x x x x x 11. ; 3 2 4 3 , 0 3 4 2 , 2 5 3 2 1 3 2 1 3 2 1 x x x x x x x x x 12. 8 2 4 4 3 3 5 2 5 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 13. 12 5 3 21 13 2 5 10 5 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 14. 7 5 5 3 7 3 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 15. 13 3 4 2 1 5 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 16. 5 3 2 3 2 2 2 2 3 4 3 2 1 3 2 1 3 2 1 x x x x x x x x x 17 1 2 14 3 5 3 10 7 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x 18. 7 4 3 2 3 7 3 7 4 6 3 2 1 3 2 1 3 2 1 x x x x x x x x x 19. 10 4 3 2 0 3 2 14 5 2 3 3 2 1 3 2 1 3 2 1 x x x x x x x x x 20. ; 15 2 3 4 , 1 3 5 2 , 9 2 6 5 3 2 1 3 2 1 3 2 1 x x x x x x x x x 6- mashg’ulot. Tekislikda analitik geometriya 1. Tekislikda analitik geometriyaning sodda masalalari mavzusibo’yicha mu sta qil bajarish uchun m asalalar 1.Son o ’qida 4 , 5 B A va 2 C nuqt alar yasalsin va kesma larning shu o ’qdagi AV, VS va AS katt alik lar i to pilsin. AC BC AB ek anlig i t ek shir ils in. 2.Old ing i mashq 4 , 1 B A va 5 C nuqtalar uchun ba jar ilsin. 3. Uchlar i 1 ; 0 , 2 ; 4 B A va 3 ; 3 C nuqt alarda bo ’lgan uc hburchak ning perimet rini to ping. 4. 1 ; 2 A nuqt adan am, Ou o ’qdan am 5 bir likk a u zoqlashgan nuqt a topilsin. 5. Ox o ’qida 4 ; 8 A nuqt adan va koordinat lar bo shidan baravar uzoqlikda t urgan nuqt a topilsin. 6. Uchlar i 2 ; 3 , 3 ; 4 B A va 6 ; 1 C nuqt alarda bo ’lgan uchburchakka tashq i chiz ilga n do iraning markaz i va radius i to pils in. 7.Ordinat a lar o ’qida koordinat lar bo shida n va 5 ; 2 A nuqtad an baravar uzo qlikda t urgan nuqta topils in. 8.Abssissa lar o ’qida 3 ; 2 A nuqt adan 5 3 bir likka uzoqlashgan nuqt a topils in. 9. 1 ; 3 A va 3 ; 5 B nuqt alar o rasidagi maso fani t oping. 10. 3 ; 5 A va 4 ; 6 B nuqt alar or asidag i masofa ni to ping. 11. 1 ; 2 A va 6 ; 3 B nuqtalar yasalsin. AV kesma ni 2 : 3 : NB AN nisbat da bo ’luvc hi y x N ; nu qt a t op ils in. 12. 1 ; 2 A va 6 ; 3 B nuqtalar ya sa lsin. AV kesma ni 1 : 2 : MB AM nisb atda bo ’luvc hi y x M ; nuqt a topilsin. 65 13. Uchlar i 3 ; 4 , 1 ; 2 B A va 1 ; 2 C nuqt alarda bo ’lgan uchburchak to mo nlar ining o ’rtalar i aniq la ns in. 14. Uchlar i 0 ; 8 , 0 ; 0 A O va 6 ; 0 B nuqt alarda bo ’lgan uchburchakda OS media na va OD bissektr isa u zunlik lar i aniq lansin. 15. Uchlar i 3 ; 5 , 0 ; 2 B A va 6 ; 2 C nuqt alarda bo ’lgan uchburchakning yuz i hisoblansin. 16.Uchlar i 3 ; 6 , 6 ; 4 , 1 ; 3 C B A va 2 ; 5 D nuqtalard a bo ’lgan to ’rtburchakning yuz i hisobla n. 7-mashg’ulot. To’g’ri chiziq va uning tenglamalari m avzusibo’yicha mustaqil bajarish uchun masalalar 1. OY o’qidan 4 b kesama ajratib OX o’qi bilan 0 135 burchak tashkil etuvchi to’g’ri chiziqni yasang va uning tenglamasini yozing. 2. OY o’qidan 2 b kesma ajratib OX o’qi bilan 0 60 burchak tashkil etuvchi to’g’ri chiziqni yasang va uning tenglamasini yozing. 3. Koordinatlar boshidan o’tib, OX o’qi bilan: 0 0 0 0 90 ). 4 , 60 ). 3 , 120 ). 2 , 45 ). 1 burchak tashkil etuvchi to’g’ri chiziqlarni yasang va ularning tenglamalarini yozing. 4. 1) 0 15 5 3 y x ; 2) 0 2 3 y x ; 3) 2 y ; 4) 1 4 / 4 / y x to’g’ri chiziqlar uchun k va b parametrlarni aniqlang. 5. 1) 0 12 3 4 y x ; 2) 0 3 4 y x ; 3) 0 7 2x ; 4) 0 7 2 y to’g’ri chiziqlarning kesmalarga nisbatan tenglamalarini yozing va ularni yasang. 6. ) 3 ; 2 ( A nuqtadan o’tib, OX o’qi bilan 0 60 burchak hosil qiluvchi to’g’ri chiziqni yasang va uning tenglamasini yozing. 7. 1) 0 6 3 2 y x ; 2) 0 4 2 3 y x to’g’ri chiziq tenglamalarini, kesmalar bo’yicha tenglamasiga keltiring. 8. 0 40 5 y Ax to’g’ri chiziq A ning qanday qiymatlarida koordinat o’qlaridan bir xil kesmalar ajratadi. 9. Uchlari ) 4 ; 3 ( A , ) 2 ; 3 ( B va ) 2 ; 1 ( C nuqtalarda bo’lgan uchburchak tomonlarining tenglamalarini yozing. 10. To’g’ri chiziqning koordinatlar boshidan uzoqligi 3, unga koordinatlar boshidan tushirilgan perpendikulyar OX o’qi bilan 0 45 burchak hosil qilsa, to’g’ri chiziq tenglamasini yozing. 11. 0 3 y x to’g’ri chiziqqa koordinatlar boshidan tushirilgan perpendikulyarning uzunligini va uning OX o’qi bilan tashkil qilgan burchagini toping. 12. Ushbu 1) 0 6 4 3 5 2 y x , 2) 0 7 13 5 13 12 x 3) 0 2 4 3 5 3 y x , 4) 0 4 3 2 3 1 y x to’g’ri chiziq tenglamalaridan qaysilari normal ko’rinishda? 13. Ushbu 1) 0 26 12 5 y x , 2) 0 10 4 3 y x , 3) 5 3x y , 4) 0 7 2 2 y x to’g’ri chiziq tenglamalarini normal ko’rinishga keltiring. Download 1.79 Mb. Do'stlaringiz bilan baham: |
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