Synergy Linear Algebra
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Синергия Линейная алгебра.doc (416.50 KB)
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- 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
Additional information
- 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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