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
75. The matrix equation A * X = B has a solution
76. Find A B, where;
77. Find the inverse of the matrix
78. Solve the matrix equation AX AXA = B, where; ...
79. Expand the determinant
80. Indicate the equation of the circle, the center of which coincides with the origin, and the straight line 3x-4y 20 = 0 is tangent to the circle
81. At what positive value of the parameter t are the straight lines given by the equations 3tx-8y 1 = 0 and (1 t) x-2ty = 0 parallel?
82. The vertices of the triangle ABC are given:
A (3; -1), B (4; 2) and C (-2; 0). Write the equations of its sides
83. Find the coordinates of the point K of the intersection of the straight line with the plane 2x 5y- 3z = 0
84. Specify the equation of the circle passing through the point (4; 5) with the center at the point (1; -3)
85. Find the coordinates of the point of intersection of lines 2x-y- 3 = 0 and 4x 3y- 11 = 0
86. Find the equation of the straight line passing through the points M1 (3; 2), M2 (4; -1)
87. Equation 3x - 4y 12 = 0 transform to an equation in line segments
88. Determine the semiaxes of the hyperbola
89. Indicate the equation of a circle for which points A (3; 2) and B (-1; 6) are the ends of one of the diameters
90. Indicate the equation of a parabola with apex at point O and focus F (4; 0)
91. Determine the semiaxes of the hyperbola 25x2 - 16y2 = 1
92. Given are straight lines and At what value of α are they perpendicular?
93. Make the equation of the plane passing through parallel lines and
94. At what positive value of the parameter t are the straight lines given by the equations 3tx - 8y 1 = 0 and (1 t) x - 2ty = 0 parallel?
95. Which of the following numbers is irrational?
96. The determinant of the system of three linear inhomogeneous equations with three unknowns is 5. This means that
97. 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
98. 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
99. Determine the eccentricity of an equilateral hyperbola
100. Specify the equation of the circle that passes through point A (2; 6) and its center coincides with point C (-1; 2)
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