$$$1. Calculate the determinant: 
$$ -12
$ -4
$ 8
$ 2
$$$2. Solve the equation: 
$$ -4
$ 10
$ 12
$ -6
$$$3. Find the algebraic complement of 
of matrix: А = 
.
$$ 1
$ -1
$ 2
$ -2
$$$4. Solve the equation: 
$$ 0; 1
$ -1; -2
$ 1; 1
$ 2; 2
$$$5. Find the minor of 
of the matrix: А= 
$$ 7
$ -5
$ 9
$ -7
$$$6. Calculate the determinant 
$$ 47
$ 32
$ -32
$ 87
$$$7. Select an expression corresponding to the element 
: 
$$ 
$ 
$ 
$ 
$$$8. Calculate the determinant: 
$$ 0
$ 
$ 
$ 
$$$9. For what values of λ the matrix 
has no inverse matrix?
$$ 8; -1
$ 1
$ -3; 2
$ 0
$$$10. Find the rank of matrix: 
$$ 2
$ 3
$ 1
$ 4
$$$11. Solve the system of equations by Cramer: 
$$ 
$ 
$ 
$ 
$$$12. What is a rank of matrix?
$$ The maximal order of a nonzero minor of this matrix.
$ The maximal order of a non equal to one minor of this matrix.
$ The lowest order of a nonzero minor of this matrix.
$ The lowest order of a non equal to one minor of this matrix.
$$$13. Which system of equations is said to be consistent?
$$ If it has at least one solution.
$ If it has more than one solution.
$ If it has no more than two solutions.
$ If it has at least two solutions.
$$$14. Which system of equations is said to be inconsistent?
$$ If it has more than one solution.
$ If it has at least one solution.
$ If it has no more than two solutions.
$ If it has at least two solutions.
$$$15. Methods for solving systems of linear equations.
$$ The Cramer, Gauss, inverse matrix.
$ The triangle rule.
$ The row or column expansion.
$ Reduction of order.
$$$16 What is a transpose matrix?
$$ A matrix which is formed by turning all the rows of a given matrix into columns and vice-versa.
$ A matrix in which diagonal elements are zero.
$ A matrix in which rows and columns contain null elements.
$ A matrix in which diagonal elements are equal to one.
$$$17. What is an identity matrix?
$$ The n×n square matrix with ones on the main diagonal and zeros elsewhere.
$ The n×n square matrix with ones elsewhere.
$ The n×n square matrix with zeros on the main diagonal.
$ The n×n square matrix with number on the main diagonal.
$$$18. What is a minor of 
of the matrix n-th order?
$$Determinant of order (n − 1) that is formed by deleting the i th row and the j th
column from the determinant of n -th order.
$ Determinant of n- th order that is formed by deleting the i th row and the j th
column from the determinant of order (n-1).
$ Determinant of order (n + 1) that is formed by deleting the i th row and the j th
column from the determinant of n -th order
$ Determinant of n- th order that is formed by deleting the i th row and the j th
column from the determinant of n -th order.
$$$19. Calculate the determinant: 
$$ 12
$ 14
$ 10
$ 16
$$$20. Solve the given system: 
$$ 
$ 
$ 
$ 
$$$21. Select the expression for the minor of the element а32: 
$$ 10
$ 6
$ 12
$ 7
$$$22. Calculate the determinant: 
$$ 70
$ 0
$ 14
$ 100
$$$23. Calculate the determinant: 
$$ 0
$ 
$ 1
$ 
$$$24. The indefinite integral of 
is called …
$$ set of all antiderivatives of the continuous function.
$ antiderivative of the function at the point.
$ antiderivative of the function on the interval.
$ the set of all derivatives of the continuous function.
$$$25. Solve the given system: 
$$ 
$
$
$ 
$$$26. Calculate the minor of 
of the determinant: 
$$ 1
$ -5
$ -1
$ -2
$$$27. Calculate the determinant: 
$$ -13
$ 3
$ 13
$ -3
$$$28. Find the inverse matrix 
for the given matrix 
.
$$ 
$ 
$ 
$ 
$$$29. For the consistent system of m linear equations in n unknowns it is necessary and sufficient that...
$$ 
$ 
$ 
$ 
$$$30. Calculate the determinant: 
$$ 10;
$ -12;
$ -8;
$ 14.
$$$31. Solve the equation: 
$$ 4;
$ -2;
$ 10;
$ - 4.
$$$32. Find the algebraic complement of 
of matrix 
$$ 13;
$ 0;
$ -13;
$ 12.
$$$33. Calculate: 
$$ 
$ 
$ 
$ 
$$$34. Find the minor of 
of given matrix 
: 
$$ 21;
$ -15;
$ 14;
$ -21.
$$$35. The perpendicular condition of two linears 
и 
is
$$ 
;
$ 
$ 
$ 
$$$36. The parallel condition of two linears и is
$$ 
$ 
$ 
$ 
$$$37. The 
between two linears и is equal to
$$ 
$ 
$ 
$ 
$$$38. Find the product: 
$$ 
$ 
$ 
$ 
$$$39. Find the product of matricies: 
.
$$ (15)
$ (-3)
$ (2)
$ (4)
$$$40. Find the product of matricies: 
$$ 
$ 
$ 
$ 
$$$41. The number value of second order determinant 
is equal to
$$ 
$ 
$ 
$ 
$$$42. If А-1 – is inverse matrix for A, А-1A = A А-1 and is equal to
$$ E
$ 2
$ -E
$ 0
$$$43. Calculate: 
$$ 19
$ 15
$ 37
$ -19
$$$44 A sequence 
is constant, if the set consists of...
$$ The same numbers
$ One number
$ Natural numbers
$ A whole number
$$$45. Find 
$$ 
$
$
$
$$$46. Determine the triple product of vectors: 
$$ 0
$ 2
$ 5
$ 7
$$$47. Find (ав), if 
are orthogonal vectors and 
.
$$ 0
$ 5
$ 3
$ 15
$$$48 The scalar product of two vectors 
and 
is:
$$ 
$ 
$ 
$ 
$$$49. The vector product of two vectors 
is:.
$$ 
$ 
$ 
$
$$$50. Find 
, if 
.
$$ 0
$ 0,5
$ 5
$ -1
$$$51. The vectors 
are called coplanar, if they…
$$ lie on same plane.
$ are parallel.
$ are perpendicular.
$ don’t belong.
$$$52. The sum of two vectors 
is…
$$ 
$ 
$ 
$ 
$$$53. Find the absolute value 
:
$$ 5
$ 3
$ 9
$ 4
$$$54. Let 
Find 
$$ 20
$ 10
$ 40
$ 5
$$$55. Find the cosine between two vectors 
.
$$ 0
$ 1
$ -1
$ 0,5
$$$56. The condition for coplanarity of three vectors 
determined by the equation:
$$ 
$ 
$ 
$ 
$$$57. Module of the vector product of two vectors is equal to:
$$ area of a parallelogram
$ square area
$ volume of the parallelepiped
$ sum of vectors
$$$58. Find the volume of the parallelepiped formed by unit vector 
$$ 1
$ 0
$ 3
$ -1
$$$59. Find the volume of the pyramid formed by vectors 
$$ 1/6
$ 1
$ 3/6
$ 1/5
$$$60. Find the volume of the parallelepiped formed by vectors 
$$ 36
$ 24
$ 48
$ 12
$$$61. Find 
if the vectors 
are coplanar.
$$ 0
$ 3
$ 1
$ 2
$$$62. If 
What is the area of the parallelogram formed by these vectors?
$$10
$ 20
$ 5
$ 4
$$$63. Find 
$$ -5
$ 1
$ 5
$ 9
$$$64. Find the point of intersection of the straight 
with the axis ОУ.
$$ 
$
$
$
$$$65. Find the point of intersection of the straight 
with the axis ОХ.
$$ 
$
$
$ 
$$$66. Find the coordinates of the direction vector of line: 
$$ 
$ 
$ 
$ 
$$$67. Find the coordinates of the normal vector of given plane: 
$$ 
$
$ 
$ 
$$$68. Find the point of intersection of the plane 
with the axis ОУ.
$$ 
$
$
$
$$$69. Find the point of intersection of the plane 
with the axis ОZ.
$$ 
$
$
$ 
$$$70. Given three vertices 
, 
and 
parallelogram АВСD. Find its fourth vertex D, the opposite В.
$$ 
$
$
$
$$$71. Find the equation of a plane passing through the points 
, 
, 
.
$$ 
;
$ 
;
$ 
;
$ 
.
$$$72. Determine the cosine of the angle between the planes 
and 
:
$$ 
;
$ 
;
$ 
;
$ 
.
$$$73. Given two adjacent vertices of a parallelogram 
and the intersection point of its diagonals 
. Find the other two vertices.
$$ 
$ 
$ 
$ 
$$$74. Given the vertices of a triangle 
. Find the middle line parallel to the side АС.
$$ 
$ 
$ 
$ 4
$$$75. Let the function differentiable in a neighborhood of the critical point 
and 
exist. Thereafter, if the …, than - point of maximum
$$ 
$ 
$ 
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