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1. In a homogeneous linear system with n unknowns and rank r number of basic solutions is:

n - r

2. The homogeneous system of n linear equations in n unknowns is consistent:

Always

3. Two lines are parallel if and only if the following condition:

Slope of the line are equal

4. The slope of the line is called ... inclination angle of this line to the x-axis

tangent

5. The product of two matrices exist if:

the number of columns of the first matrix are equal to the number of rows of the second matrix

6. The length of the vector is:

the square root of the sum of squares of all the coordinate

7. Two vectors are called orthogonal if their scalar product:

equal zero

8. A system of m linear equations in n unknowns called consistent if it is:

It has at least one decision

9. Three vector lying in the same plane:

always linearly dependent

10. The system of m linear equations in n unknowns called uncertain if it:

infinitely many solutions

11. The homogeneous system of n linear equations in n unknowns is uncertain:

the main determinant of the matrix of the system is equal to zero

12. A matrix is ​​called singular if its determinant

zero

13. The system of m linear equations in n unknowns called particular if it:

It has one solution

14. rank of the matrix is ​​equal to:

the number of non-zero rows, then bring it to a triangular form (?)

15. If two lines interchanged, the determinant:

changes sign

16. The system of m linear equations in n unknowns is consistent if:

Rank main matrix equals the rank of the augmented matrix

17. If a line multiplied by the determinant nonzero number k, the value of the determinant:

change in the time k

18. The eigenvectors of a linear operator corresponding to different eigenvalues ​​are necessarily

mutually orthogonal (?)

19. Two lines are perpendicular if and only if the following condition:

the product of the angular coefficients equal to -1

20. The set of all eigenvalues ​​of the linear transformation is called

spectrum

21. A matrix is ​​called the transpose if:

line change to the appropriate columns (?)

22. Make a general equation of the line passing through the point M (1,3) perpendicular to the line x + 3y = 0, 3, in the form Ax + By + C = 0.

A = 3, B = -1, C = 6 (i.e., the function 3x-y + 6 = 0)

23. Make the equation of the line passing through the points M (1, -1) and N (2,1) as a general line equation AX + By + C = 0.

A = 2, B = -1, C = -3 (i.e. function 2x-y-3 = 0)

24. Enter the equation of a line parallel to the line y = 2x-1

2 y = 4 x +3

25. Enter the equation of a line perpendicular to the line y = 5x + 3

2 y = -0,4 x +4

26. Rank nonsingular square matrix of order n is

N

27. Arithmetic n-dimensional vector is:

an ordered set of n numbers

#auto

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