Aof Panel

Soru 1

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 2

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 3

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

Soru 4

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 5

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

Soru 6

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 7

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 8

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 9

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 10

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 11

What is the value of x^.y if the matrices A and B are equal?

Soru 12

then which of the following is the entry c₃₁ of the matrix

Soru 13

Which of the following types of matrices can be multiplied by a 2x3 matrix?

Soru 14

What is the solution of the system of linear equations

Soru 15

What is the inverse of the matrix

Soru 16

What is the determinant of the coefficient matrix of the linear system

Soru 17

If the solution of the linear system

is the point (-1,3) then what is the value of m-n ?

Soru 18

What is the value of the number if the system of linear equations

has infinitely many solutions?

Soru 19

What is the type of the matrix

Soru 20

Which of the following is the determinant of the coefficient matrix of the system of linear equations

MATHEMATICS II