Synergy Linear Algebra

Synergy of MFPU MOI. Linear algebra. Answers to 100 questions. Perfectly
1. Indicate a natural series of numbers
• 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
• 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... 2, 3, 4, 5, 6, 7, 8, 9,  ...,
• -1, -2, -3, -4, -5, -6, -7, -8, -9
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
2. Vectors are called coplanar if
• they lie in the same plane
• they are perpendicular to the same plane
• they lie in the same plane or on parallel planes
3.Using Cramer´s method (determinants), one can find the solution

4. Calculate the determinant
• 56
• 42
•1
• 0

5. Calculate the determinant
• 3
• 6
• 22
•eighteen

6. Which of the following numbers is irrational?
• 1/2
• 5.4 (15)
• 3.141592 ...
• 4.99

7. Given: Find
• 32
• 40
•ten
• 20

8. How many integers satisfy the inequality -8; 4?
•nine
•12
•13
•eleven
•ten

9. Which of the listed vectors is collinear to the vector?
•

•

•

•

10. Find the angle between vectors a = 2m 4n and b = m - n, where m and n are unit vectors and the angle between m and n is 120 °
• 180
•100
• 120
• 90

11. What numbers are called integers?
• only positive numbers
• only natural numbers and numbers opposite to natural numbers
• natural numbers, numbers opposite to natural numbers, and number 0
• only numbers ending in 0

12. For what value of l are vectors and collinear if M (-3; 2), P (-1; -2) K (2; 1), D (5; l)?
• -4.5
•-5
•-4
•

13. Simplify the expression
•

•

•

•

14. Simplify an irrational expression
•
•
• -22
• 22

15. Find the value of the expression at a = 2
• 2

•

•1

•

16. Find a general solution to the system
•

•

•

•

17. Calculate
•

•

•

•

18. Given points M (-5; 7; -6), N (7; -9; 9). Calculate the projection of a vector to a vector
• 25
•4
• 75
• 3

19. Vectors and serve as diagonals of parallelogram ABCD. Express the vector in terms of vectors and
•

•

•

20. Find the meaning of the expression
•

•

•

•

21. What vectors are called collinear?
• lying on one straight line or on parallel lines

22. Calculate the determinant

23. Given: Calculate
• 144
•eleven
•13
•12

24. Evaluate the expression
• 10000
• 1000
•100
•ten

25. Which of the following fractions is a mixed periodic fraction?
• 7, (3)
• 3.14
• 8, (11)
• 2.75 (12)

26. Find
• - 2 or 2
• - 2
• 2

27. Find l if
•

• 3

• 3 or -3

•

28. Vectors and are mutually perpendicular (orthogonal), and and. Define
• 17
• 8.5
• 7
•13

29. What is called the dot product of two vectors?
30. Find l if
31. Calculate to the nearest tenth


32. Given vectors and Find - the projection of the vector onto the axis of the vector

33. A system of linear equations is called definite if

34. Establish the relative position of straight lines and

35. Find an acute angle between straight lines and °

36. Determine the equation of a straight line that cuts off the segment b = 2 on the Oy axis and makes an angle j = 45 ° with the Ox axis

37. Find the equation of the straight line passing through the point of intersection of lines
2x 3y - 8 = 0 and x - 4y 5 = 0 and through the point M1 (-2; 3)

38. Write the canonical equation of a hyperbola, the foci of which lie on the Ox axis, if given a = 6 and b = 2

39. Indicate the equation of the circle that passes through point A (3; 1), and its center lies on the straight line 3x-y- 2 = 0

40. Determine the equation of the plane, knowing that point A (1, -1,3) serves as the base of the perpendicular drawn from the origin to this plane

41. Determine the eccentricity of an equilateral hyperbola


42. Indicate the equation of the circle that passes through point A (2; 6) and its center coincides with point C (-1; 2)

43. Write the canonical equation of an ellipse if given its semiaxes a = 5 and b = 4

44. Write the equation of a circle of radius R = 8 centered at point C