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# Mathematics Seminar 108 questions with answers

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**04.07.2013**

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## Description

Mathematics Seminar 108 questions

Lesson number 1

Question №1. Complete the following sentence. The determinant ... if its swap line with the corresponding columns.

1) does not change

2) is reset

3) changes sign

Question №2. Complete the sentence. Matrix used by mathematicians for .....

1) shorthand systems of equations

2) to solve logic problems

3) to perform a comparison operation

Question №3. Complete the sentence. Determinant with two identical rows and columns is ....

1) zero

2) unity

3) 100

Question №4. As can be designated determinant of A?

3) any of the above methods

Question №5. Complete the sentence. If the elements of any row (or column) of the determinant add the corresponding elements of another row (or column) multiplied by the same number, the determinant ....

1) does not change its value

2) increase by this number

3) decrease this number

Question №6. What is the determinant of the product of matrices A and B, if detA = 3 and detB = 4?

1) 1

2) 7

3) 12

Question №7.

1) The matrix is \u200b\u200bsymmetric

2) The determinant of the matrix A is equal to zero

3) The matrix is \u200b\u200bsquare

Question №8.

1) 0

2) 2

3) 1

Question №9.

1) 1

2) 5

3) -1

Question №10. What matrix can be folded?

1) having the same size

2) having the same number of rows

3) Only non-degenerate

Question №11. What size matrix obtained by multiplying the matrix A (3x5) in the matrix (5x5)?

1) 5x5

2) 3x5

3) 5x3

Question №12. Which of the matrix is \u200b\u200bthe identity?

1)

2)

3)

Lesson number 2

Question №1. What happens when a symmetric matrix transpose it?

1) None

2) it turns in the opposite

3) changes its size

Question №2.

1)

2)

3)

Question №3.

1)

2)

3)

Question №4. What word is missing in the definition? "If the determinant of a matrix is \u200b\u200bzero, then a matrix is \u200b\u200bcalled ...."

1) transpose

2) Zero

3) the degenerate

Question №5. In which case, the product of matrices A and B, the equality AB = BA?

1) If these matrices have the same size

2) If the matrix A is the number of columns equal to the number of rows of the matrix

3)

Question №6. In any case, for the product of square matrices A and B, having the same dimensions without the equality AB = BA?

1)

2) If the matrix A - zero

3) In all these cases AB = BA

Question №7. Complete the sentence. The determinant is not equal to zero, then the inverse matrix .....

1) there is

2) is zero

3) is a unit

Question №8.

1)

2)

3)

Question №9.

1) The system has no solutions

2) The system has an infinite number of solutions

3)

Question №10.

1) 2x3

2) 3x3

3) 3x4

Question №11.

1)

2) X = AC

3) X = CA

Question №12. Enter the formula Cramer.

1)

2) X = CA

3)

Lesson number 3

Question №1. For a number of vectors can be determined by the sum rule of the polygon?

1) for any

2) 2

3) 3

Question №2. Complete the sentence. The three-dimensional basis vector can be called .....

1) any three linearly independent

2) any two linearly independent

3) Any 3

Question №3. Complete the sentence. To calculate the direction cosines of the vector necessary ....

1) use the Pythagorean Theorem

2) take the square root of the sum of the squares of its components

3) calculate the length and divide it on the projection vector on the coordinate axes

Question №4. How to change the length of the vector, if you multiply it by a scalar factor m?

1) does not change

2) to increase by m

3) decrease in the m times

Question №5. Finding the unit vector (ie the vector of length) in the same direction as the vector called .....

1) scan vectors

2) valuation vector

3) the definition of the module vktora

Question №6. How will

## Additional information

Question №7. Complete the sentence. The sum of several vectors can be called ....

1) the linear combination of the vectors

2) transplant vectors

3) deactivation vectors

Question №8. Complete the sentence. Collinear vectors is the same as ....

1) parallel vectors

2) transplant vectors

3) the sum of vectors

Question №9. Complete the sentence. The vectors are called coplanar if they ....

1) collinear

2) lie in the plane of the discharge

3) normalized

Question №10. Complete the sentence. To test the linear independence of the vectors it is necessary ....

1) calculate their scalar product

2) create a linear combination

3) calculate the determinant of a matrix whose columns are the vectors

Question №11. Complete the sentence. To determine the coefficients of the expansion of the vector in the basis it is necessary ....

1) to calculate the coefficients in the representation of this vector as a linear combination of vectors that form a basis

2) calculate their scalar product

3) calculate their cross product

Question №12. Complete the sentence. To determine the area of \u200b\u200ba parallelogram whose sides are formed by a parallel translation of the vectors A and B (ie, coincide with the vectors A and B) is enough ....

1) calculate the unit of the vector product

2) calculate their scalar product

3) calculate the coefficients in the representation of this vector as a linear combination of vectors that form a basis

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