Aof Panel

Soru 1

Which of the following goal functions yields 122 at (7, 5)?

Soru 2

Which of the following is the maximum value of f=9x+7y?

Soru 3

Which of the following goal functions yields the value 88 at (9, 4)?

Soru 4

Soru 5

What is the antiderivative of ∫ 2 lnx dx equal to?

Soru 6

I. Let m and n be positive integers. An m×n matrix is a rectangular array of mn numbers enclosed in brackets.

II. For an m×n matrix these mn numbers are called entries of this matrix.

III. Matrices are denoted by lowercase letters and entries of matrices are denoted by capital letters always.

What can be said to be true about matrices?

Soru 7

If the matrices A = [2 3 4, 5 6 7] and B = [x 3 2.y, 5 3.z 7] and A and B matrices are equal, then what is the value of x + y + z?

Soru 8

For the matrices, A = [2 3 , 5 6 ]_2x2 and B = [1 3, 3 7]_2x2what is the multiplication of these two matrices?

Soru 9

I. If there exists a square matrix A-1 such that A.A^-1 = I_n = A^-1.A, then the matrix A^-1 is called the inverse matrix of A.

II. If a matrix A has an inverse, A is called invertible if such an inverse does not exist, A is called singular.

III. The inverse matrix can be defined for a nonsquare matrix also all square matrices possess inverses.

What can be said to be true about inverse matrices?

Soru 10

For the matrices, A = [2 3 , 5 6 ]_2x2 and B = [1 3, 3 7]_2x2what is the sum of these two matrices?

Soru 11

I. The lines may intersect at only one point, in which case the system has exactly one solution.

II. The lines may be parallel and distinct, in which case there is an intersection point therefore
the system has one solution.

III. The lines may coincide, in which case there are infinitely many intersection points and
consequently the system has infinitely many solutions.

For a system of linear equations with graphs of these equations' lines in the xy-plane what can be said to be true?

Soru 12

For the given the linear system
4x + 6y = 10
6x – 4y = 2

which of the given x and y pairs is the solution of the linear system

Soru 13

I. Cramer’s rule is used to solve a system of linear equations in three unknowns with a nonsingular coefficient matrix.

II. The method of finding solutions of systems of linear equations using determinants of matrices is called the Cramer method.

III. Cramer’s rule can be applied to the linear systems which consist of two unknowns or more than two unknowns.

What can be said to be true about Cramer's rule?

Soru 14

I. The first two columns of the matrix are written to the right of the original matrix A, and each
diagonal is multiplied.

II. The descending diagonals from left to right has negative sign while the descending diagonals from right to left has a positive sign.

III. To obtain the determinant of the matrix, the results of the multiplications are added by taking into account the signs.

What can be said to be true about Sarrus' rule?

Soru 15

I. det(AB) = det A . det B

II. det(A + B) = detA + detB

III. det(A + B) ≠ detA + detB

Which of the given equalities about the determinant of a matrix can be said to be true?

Soru 16

I. A linear programming problem includes a linear function in two variables that we want to maximize or minimize.

II. a linear function in two variables that we want to maximize or minimize is called the goal function.

III. The system of linear inequalities in a linear programming problem is also called the Corner Point.

What can be said to be true about linear programming problems?

Soru 17

Where will the maximum or minimum of a linear function over the constrained set if it exists will necessarily occur, according to the corner point theorem ?

Soru 18

I. To guarantee the boundedness of the constraint set in the sequel, we assume that a₁ ≥ 0,…, a_m ≥ 0, b₁ > 0,…, b_m > 0, c₁ > 0,…, c_m > 0.

II. The constraint set is bounded and is called a polygonal set with infinite number of corner points.

III. The corner points of the constraint set are the intersection points of the straight lines.

What can be said to be true in the case of n = 2, the linear programming problem consists of the maximization of linear, two variable function f = ax + by under the system of linear inequalities in two variables?

Soru 19

Which of the following points belongs to the set specified by the inequality 2x + 7y + 1 ≥ 25?

Soru 20

Which of the following points belongs to the set specified by the inequality 5x + 2y ≤ 10?

MATHEMATICS II - Deneme Sınavı - 13