Amaliy Matematika Yakuniy Savollar PDF
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This document contains a collection of questions on matrix operations, linear equations systems, and quadratic forms. The questions are suitable for university-level students.
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1. a) Matritsalar ustida amallarni bajaring. 1 2 3 9 8 7 1. A = 4 5 6 , B = 6 5 4 2 AT + AB = ? 7 8 9 3 2 1 3 5 7 1 2 3 2. A = 2 ...
1. a) Matritsalar ustida amallarni bajaring. 1 2 3 9 8 7 1. A = 4 5 6 , B = 6 5 4 2 AT + AB = ? 7 8 9 3 2 1 3 5 7 1 2 3 2. A = 2 4 6 , B = 4 5 6 3 A + 2 BA = ? 1 3 5 7 8 9 2 0 8 2 3 4 3. A = −3 5 4 , B = 1 0 −1 3 AT B − 4B = ? 5 −3 4 7 −2 3 1 2 1 2 0 1 4. A = 0 1 0 , B = 3 1 0 −5 AT + 4 AB = ? 2 3 4 1 0 1 3 6 9 5 1 −2 5. A = 2 4 8 , B = −3 2 7 3 A + ABT 1 5 7 4 0 −1 1 1 1 9 8 7 6. A = 2 2 2 , B = 6 5 4 −2 AT − 5 AB = ? 3 3 3 3 2 1 9 8 7 1 1 1 7. A = 6 5 4 , B = 2 2 2 − AT + ABT = ? 3 2 1 3 3 3 1 2 3 9 8 7 8. A = 4 5 6 , B = 6 5 4 3 A − 2 AT B = ? 7 8 9 3 2 1 4 5 6 1 5 −2 9. A = 1 2 3 , B = 7 9 3 −3 A + 2 AT BT = ? 7 8 9 8 −4 1 5 4 3 3 2 1 10. A = 2 1 0 , B = 4 3 2 BT − 2 AB = ? 1 2 3 5 4 3 8 7 6 1 2 3 11. A = 5 4 3 , B = 4 5 6 3 AT + 2 AB = ? 2 1 0 7 8 9 1 1 1 9 8 7 12. A = 2 2 2 , B = 6 5 4 −5 A + 3 ABT = ? 3 3 3 3 2 1 7 6 5 −1 2 4 13. A = 4 3 2 , B = 5 −1 0 3 AT + 3BT A = ? 1 0 1 3 1 8 2 3 4 1 2 3 14. A = 5 6 7 , B = 4 5 6 ABT + AT = ? 8 9 1 7 8 9 9 8 7 2 3 4 15. A = 6 5 4 , B = 5 6 7 3 A + 4BAT = ? 3 2 1 8 9 0 1 2 3 1 0 1 16. A = 45 6 , B = 0 1 0 2 AT − 4BA = ? 7 8 9 1 0 1 5 5 5 2 −1 1 17. A = 4 4 4 , B = 2 4 5 −3 A + 5 AB = ? 3 3 3 −3 5 3 4 3 2 1 2 3 18. A = 1 0 1 , B = 4 5 6 3 AT − 4 ABT = ? 2 3 4 7 8 9 3 4 5 1 2 3 19. A = 6 7 8 , B = 4 5 6 4 AB + 2BT = ? 9 1 2 7 8 9 1 1 1 1 2 3 20. A = 2 2 2 , B = 4 5 6 AT + ABT = ? 3 3 3 7 8 9 2 4 6 1 0 3 21. A = 1 3 5 , B = 2 1 4 BT − BT AT = ? 79 11 5 6 7 5 6 7 2 1 3 22. A = 8 9 10 , B = 4 2 6 −2 AT − 3 AB = ? 11 12 13 7 3 9 3 5 7 3 0 8 23. A = 1 2 4 , B = −1 4 1 AT − 3BBT = ? 6 8 9 5 −3 5 1 2 3 9 8 7 24. A = 4 5 6 , B = 6 5 4 3BAT + 2BT = ? 7 8 9 3 2 1 2 4 6 4 −1 0 25. A = 1 3 5 , B = 7 1 5 5BT − 4BA = ? 0 1 2 1 2 −1 2 3 1 1 2 3 26. A = 4 5 6 , B = 4 5 6 2BT + 3 AB = ? 7 8 9 7 8 9 8 7 6 1 2 3 27. A = 54 3 , B = 4 5 6 5 ABT + A = ? 2 1 0 7 8 9 1 3 5 −1 2 7 28. A = 2 4 6 , B = 6 5 −2 6 AT BT − A = ? 7 8 9 3 −1 4 0 1 2 2 0 1 29. A = 3 4 5 , B = 3 2 4 2 AT + 7 ABT = ? 6 7 8 5 6 7 6 5 4 1 2 3 30. A = 3 2 1 , B = 4 5 6 3 AB − BT = ? 0 1 2 7 8 9 b) 1. Chiziqli tenglamalar sistemasini yeching: x1 + 2 x2 + 3x3 = 9 2 x1 + 3x2 + x3 = 8 3x + x + 2 x = 7 1 2 3 2. Chiziqli tenglamalar sistemasini yeching: 2 x1 − x2 + 3 x3 = 5 4 x1 + 2 x2 + x3 = 1 3 x + x + 2 x = 3 1 2 3 3. Chiziqli tenglamalar sistemasini yeching: x1 + x2 + x3 = 3 2 x1 + 3x2 + 4 x3 = 10 3x + 2 x + x = 5 1 2 3 4. Chiziqli tenglamalar sistemasini yeching: 3x1 + x2 − x3 = 4 x1 + 2 x2 + 3x3 = 10 2 x − x + 4 x = 5 1 2 3 5. Chiziqli tenglamalar sistemasini yeching: x1 − 2 x2 + 4 x3 = 8 3 x1 + x2 + x3 = 6 2 x + 3x − x = 1 1 2 3 6. Chiziqli tenglamalar sistemasini yeching: 4 x1 + 3x2 + 2 x3 = 12 2 x1 − x2 + 3x3 = 3 x + 4 x + 2 x = 10 1 2 3 7. Chiziqli tenglamalar sistemasini yeching: 5 x1 + 2 x2 + x3 = 14 3x1 − x2 + 2 x3 = 3 2 x + 4 x + 3x = 12 1 2 3 8. Chiziqli tenglamalar sistemasini yeching: 2 x1 + x2 + 3x3 = 7 x1 − x2 + 2 x3 = 3 4 x + 3x + x = 5 1 2 3 9. Chiziqli tenglamalar sistemasini yeching: 3 x1 + 4 x2 + 5 x3 = 20 2 x1 + 3x2 + 4 x3 = 10 x + x + x = 3 1 2 3 10. Chiziqli tenglamalar sistemasini yeching: x1 + 3 x2 + 2 x3 = 1 2 x1 − x2 + 4 x3 = 8 3 x + 2 x + 3 x = 7 1 2 3 11. Chiziqli tenglamalar sistemasini yeching: 4 x1 + x2 − x3 = 3 x1 + 5 x2 + 3 x3 = 12 2 x + 3x + 4 x = 9 1 2 3 12. Chiziqli tenglamalar sistemasini yeching: x1 + 2 x2 + 3x3 = 9 3x1 + 4 x2 + x3 = 11 2 x + x + 2 x = 5 1 2 3 13. Chiziqli tenglamalar sistemasini yeching: 2 x1 + x2 + 5 x3 = 8 3x1 − x2 + 4 x3 = 10 x + 4x + 2x = 6 1 2 3 14. Chiziqli tenglamalar sistemasini yeching: x1 − x2 + 2 x3 = 5 2 x1 + 3x2 + x3 = 7 3 x − 2 x + 4 x = 8 1 2 3 15. Chiziqli tenglamalar sistemasini yeching: 4 x1 + 2 x2 + 3x3 = 14 x1 + x2 + x3 = 5 3x + 4 x + 2 x = 11 1 2 3 16. Chiziqli tenglamalar sistemasini yeching: x1 + 4 x2 + 5 x3 = 20 3 x1 + 2 x2 + x3 = 7 4 x − x + 3x = 10 1 2 3 17. Chiziqli tenglamalar sistemasini yeching: 2 x1 + 3x2 + x3 = 6 3x1 + x2 + 4 x3 = 8 x + 2 x + 5 x = 11 1 2 3 18. Chiziqli tenglamalar sistemasini yeching: x1 + 2 x2 + 4 x3 = 10 2 x1 − x2 + 3x3 = 5 3 x + 4 x + x = 8 1 2 3 19. Chiziqli tenglamalar sistemasini yeching: 4 x1 + 5 x2 + 2 x3 = 12 3 x1 + 2 x2 + 3 x3 = 10 x + 4 x + 5 x = 15 1 2 3 20. Chiziqli tenglamalar sistemasini yeching: x1 − 2 x2 + x3 = 4 2 x1 + 3x2 + 5 x3 = 6 3 x + 4 x − x = 10 1 2 3 21. Chiziqli tenglamalar sistemasini yeching: 3 x1 + 4 x2 + x3 = 7 x1 − x2 + 2 x3 = 3 2 x + 5 x + 3x = 6 1 2 3 22. Chiziqli tenglamalar sistemasini yeching: x1 + x2 + x3 = 6 2 x1 + 3x2 + 4 x3 = 12 3x + 2 x + 5 x = 10 1 2 3 23. Chiziqli tenglamalar sistemasini yeching: x1 + 2 x2 + 3x3 = 9 3x1 + 4 x2 + x3 = 10 2 x − x + x = 2 1 2 3 24. Chiziqli tenglamalar sistemasini yeching: 2 x1 + x2 + 3x3 = 5 x1 − x2 + 2 x3 = 6 3 x + 4 x + x = 8 1 2 3 25. Chiziqli tenglamalar sistemasini yeching: 4 x1 + 2 x2 + x3 = 10 x1 + 3 x2 + 4 x3 = 11 2 x + x + 3x = 7 1 2 3 26. Chiziqli tenglamalar sistemasini yeching: 3 x1 + 4 x2 − x3 = 5 2 x1 + x2 + 3x3 = 8 x + 3x + 2 x = 6 1 2 3 27. Chiziqli tenglamalar sistemasini yeching: x1 + 2 x2 + x3 = 4 2 x1 + 3x2 + 4 x3 = 10 3x + x + 2 x = 5 1 2 3 28. Chiziqli tenglamalar sistemasini yeching: x1 − 3x2 + 2 x3 = 5 2 x1 + 4 x2 + 3x3 = 12 3x + 2 x − x = 1 1 2 3 29. Chiziqli tenglamalar sistemasini yeching: 4 x1 + 5 x2 + 2 x3 = 20 2 x1 + 3 x2 + 4 x3 = 10 x + x + x = 3 1 2 3 30. Chiziqli tenglamalar sistemasini yeching: 5 x1 + x2 − 2 x3 = 7 3x1 + 4 x2 + x3 = 12 x + 2 x + 3x = 8 1 2 3 3. Kvadratik formalar. x = 3 y1 − 3 y2 1. f ( x1; x2 ) = 2 x12 − 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −3 y1 + 3 y2 2. f ( x1; x2 ) = 2 x12 + 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2x = y1 + 3 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 3 y1 + y2 3. f ( x1; x2 ) = −2 x12 − 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 − 3 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 + 3 y2 4. f ( x1; x2 ) = −2 x12 + 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = −3 y1 + 3 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 3 y1 − 3 y2 5. f ( x1; x2 ) = 2 x12 − 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = 2 y1 + 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −3 y1 + 2 y2 6. f ( x1; x2 ) = 2 x12 + 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 + 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + 3 y2 7. f ( x1; x2 ) = −2 x12 − 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 − 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 3 y1 + 2 y2 8. f ( x1; x2 ) = −2 x12 + 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = −2 y1 + 3 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 − 3 y2 9. f ( x1; x2 ) = 2 x12 − 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 2 y1 + 3 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −2 y1 + 2 y2 10. f ( x1; x2 ) = 2 x12 + 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 + 3 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 3 y1 + 2 y2 11. f ( x1; x2 ) = −2 x12 − 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 2 y1 − 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + 3 y2 12. f ( x1; x2 ) = −2 x12 + 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = − 2 y1 + 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 − 2 y2 13. f ( x1; x2 ) = 2 x12 − 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 3 y1 + 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −2 y1 + 2 y2 14. f ( x1; x2 ) = 2 x12 + 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 2 y1 + 3 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + 2 y2 15. f ( x1; x2 ) = − x12 − 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = 2 y1 − 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + 2 y2 16. f ( x1; x2 ) = − x12 + 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = −2 y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 − 2 y2 17. f ( x1; x2 ) = x12 − 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = y1 + 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −2 y1 + y2 18. f ( x1; x2 ) = x12 + 2 x1x2 − 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = 2 y1 + 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 + 2 y2 19. f ( x1; x2 ) = − x12 − 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 2 y1 − 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + 2 y2 20. f ( x1; x2 ) = − x12 + 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = − y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 − y2 21. f ( x1; x2 ) = x12 − 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli x2 = 2 y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = − y1 + 2 y2 22. f ( x1; x2 ) = x12 + 2 x1x2 + 2 x2 2 kvadratik forma berilgan. 1 chiziqli 2x = 2 y1 + y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = 2 y1 + y2 23. f ( x1; x2 ) = − x12 − 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = y1 − 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 + 2 y2 24. f ( x1; x2 ) = − x12 + 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = − y1 + 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 − y2 25. f ( x1; x2 ) = x12 − 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = 2 y1 + 2 y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = −2 y1 + y2 26. f ( x1; x2 ) = x12 + 2 x1x2 − x2 2 kvadratik forma berilgan. 1 chiziqli x2 = y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 + 2 y2 27. f ( x1; x2 ) = − x12 − 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = y1 − y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y1 + y2 28. f ( x1; x2 ) = − x12 + 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli 2 x = −2 y1 + y 2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = y − y2 29. f ( x1; x2 ) = x12 − 2 x1x2 + x2 2 kvadratik forma berilgan. 1 1 chiziqli x2 = y1 + 2 y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. x = − y1 + y2 30. f ( x1; x2 ) = x12 + 2 x1x2 + x2 2 kvadratik forma berilgan. 1 chiziqli x2 = y1 + y2 almashtirish orqali hosil bo’lgan f ( y1; y2 ) kvadratik formani toping. 3. Analitik geometriya elementlari. a) 1. M 0 ( 4;5) nuqtadan o‘tuvchi va l ( −8;3) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 2. M 0 ( 4;2 ) nuqtadan o‘tuvchi va l ( −2;3) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 3. M 0 ( 9;5) nuqtadan o‘tuvchi va l ( 7;4 ) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 4. M 0 ( 4; −3) nuqtadan o‘tuvchi va l ( 5;6) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 5. M 0 ( −4 − 6 ) nuqtadan o‘tuvchi va l (1;2 ) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 6. M 0 ( −6;4 ) nuqtadan o‘tuvchi va l ( 5;2) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 7. M 0 ( 7;4 ) nuqtadan o‘tuvchi va l ( −5; −3) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 8. M 0 ( 9;7 ) nuqtadan o‘tuvchi va l ( −3;4 ) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 9. M 0 ( 4;5) nuqtadan o‘tuvchi va l ( −2;3) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 10. M 0 ( 7;9 ) nuqtadan o‘tuvchi va l ( −5;4 ) vektorga parallel bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 11. M 0 ( 2;4 ) nuqtadan o‘tuvchi va n ( 5;7 ) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 12. M 0 ( −5; −6 ) nuqtadan o‘tuvchi va n ( 8;7 ) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 13. M 0 ( −2; −7 ) nuqtadan o‘tuvchi va n ( 3;9 ) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 14. M 0 (1;4 ) nuqtadan o‘tuvchi va n ( 2; −3) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 15. M 0 ( −7; −4 ) nuqtadan o‘tuvchi va n ( 2;3) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 16. M 0 ( 5;1) nuqtadan o‘tuvchi va n ( 7;5 ) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 17. M 0 ( −7;6 ) nuqtadan o‘tuvchi va n (10;13) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 18. M 0 ( −4;5) nuqtadan o‘tuvchi va n (8;3) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 19. M 0 ( 7; −2 ) nuqtadan o‘tuvchi va n (1; −11) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 20. M 0 ( −1; −5) nuqtadan o‘tuvchi va n (8;3) vektorga perpendikulyar bo‘lgan to‘g‘ri chiziq tenglamasini tuzing. 21. M 0 ( 4;6 ) nuqtadan −5 x + 2 y + 1 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 22. M 0 ( −3;2 ) nuqtadan 3x + 4 y − 3 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 23. M 0 ( 7;5) nuqtadan −9 x + 2 y + 9 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 24. M 0 ( −4;5) nuqtadan 4 x + y − 6 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 25. M 0 ( −2;4 ) nuqtadan −5 x + 2 y + 1 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 26. M 0 ( 9;4 ) nuqtadan 2 x + 4 y − 4 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 27. M 0 ( −2;2 ) nuqtadan 5 x + 3 y − 4 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 28. M 0 ( 3;1) nuqtadan 5 x − 4 y + 3 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 29. M 0 ( −2;3) nuqtadan 2 x − 5 y + 7 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping. 30. M 0 (11; −2 ) nuqtadan x − 2 y + 2 = 0 to‘g‘ri chiziqqacha bo‘lgan masofani toping.
