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# Math test responses of the 5 105 questions

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**04.07.2013**

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# Description

Task 1

Question 1: What is the Matrix?

1. number;

2. Table;

3. vector;

4. function;

5. there is no right answer.

Question 2. What are the numbers in the index at the elements of the matrix?

1. degree;

2. The number of rows and columns;

3. The order of the matrix;

4. The number for which you need to multiply the series element;

5. there is no right answer.

Question 3. How do you know the properties of determinants?

1. 0;

2. 5;

3. 1;

4. 2;

5. 3.

Question 4: What is the record size of the matrix (2x4)?

1. zero matrix;

2. square matrix;

3. The matrix has two rows and four columns;

4. The determinant of the matrix is \u200b\u200bequal to 24;

5. there is no right answer.

Question 5. Will the determinant of the second order, if swap line with the corresponding columns?

1. No

2. yes

3. Yes, if one of the elements of any row is 0

4. The correct answer is 2, and 3

5. no right answer

Task 2

Question 1. What is Minor M11 matrix (3x3)?

1. determinant obtained by calculating the determinant of our matrix by removing the first row and the first column;

2. determinant equal to zero;

3. determinant obtained by calculating the determinant of our matrix by removing the second row and the third column;

4. determinant obtained by calculating the determinant of our matrix by removing the second row and the third column, taken with a minus sign;

5. there is no right answer.

Question 2. How to get the M23?

1. The matrix multiply by two;

2. calculate the determinant of the matrix by removing the 1st row and the first column;

3. there is no right answer;

4. calculate the determinant obtained by deletion of the second row and the third column.

5. All the answers are correct

Question 3. What is the cofactor?

1. Mji;

2. Aik = (- 1) i + to Mik;

3. The determinant of the matrix;

4. The order of the matrix;

5. there is no right answer.

Question 4. Check expansion formula of the determinant of order 3 on the second line?

1. = a11A11 + A12 + A12 a13A13;

2. = a21A21 + A22 + A22 a23A23;

3. = a21A13 + A22 + A23 a31A33;

4. = a11A23 + A12 + A13 a12A33;

5. there is no right answer.

Question 5: Is it possible to expand the determinant of the fourth order in the first line?

1. no;

2. if the 1-th element is not 0;

3. sometimes;

4. there is no right answer;

5. Yes.

Activity 3

Question 1: Is it possible to add up the matrix A (2x3) and B (2x3)?

1. no;

2. Yes;

3. Only if all the elements of the matrix B = 1;

4. occasionally;

5. there is no right answer.

Question 2: Is it possible to add up the matrix A (2x3) and B (3x4)?

1. yes;

2. No;

3. always;

4. occasionally;

5. there is no right answer.

Question 3. What is the matrix is \u200b\u200bcalled a square?

1. matrix in which the number of rows equals the number of columns;

2. symmetric;

3. The matrix in which the number of lines greater than the number of columns;

4. matrix whose number of rows is less than the number of columns;

5. there is no right answer.

Question 4: Is it possible to multiply the matrix A (2x2) by the number of C?

1. no;

2. Yes, but only if a = 0;

3. yes, wherein the determinant time increase in C;

4. there is no correct answer.

5. Yes.

Question 5. Can I deduct the matrix A (2x3) of the matrix B (2x3)?

1. no;

2. always;

3. sometimes;

4. All the answers are correct

5. there is no right answer.

Task 4

Question 1. What is zero - matrix?

1. The rectangular matrix;

2. matrix, all elements of which - zero;

3. The matrix, which is on the main diagonal are zeros;

4. The identity matrix;

5. there is no right answer.

Question 2: Is it possible to multiply the matrix A (2x2) and B (2x2)?

Question 3: Is it possible to multiply the matrix A (3x4) and B (4x2)?

Question 4: Is it possible to multiply the matrix

# Additional information

Question. 2. What is the determinant of the identity matrix?

1. 0;

2. 1;

3. 2;

4. 3;

5. 18.

Question 3. What is the matrix transpose?

1. reset;

2. The element number ij ji put into place, and vice versa;

3. Multiply the matrix E;

4. elements numbered ii equal to zero

5. elements numbered ii set equal to 1.

Question 4. What is an element of the transposed matrix?

1. vij-1;

2. vij;

3. * ij;

4. 5 vij;

5. there is no right answer.

Question 5: What is the product A • A-1?

1. 0;

2. E;

3. A +;

4. A *.

5. no right answer

Task 6.

Question 1: Is it possible to find the inverse of a matrix, the matrix having = 0?

1. you can;

2. No;

3. always;

4. occasionally;

5. there is no right answer.

Question 2. What is the matrix of the system?

1. Zero Matica;

2. The matrix E;

3. The matrix consisting of the coefficients of the free terms;

4. there is no right answer;

5. Matitsa consisting of coefficients of the left side.

Question 3. What is matichnoe equation?

1. The equation of the form ax2 + Bx + C = 0;

2. The equation of the form x = A • C, where A, X, C - a matrix;

3. The equation of the form y = kx + B;

4. The equation of the form 2 + 2 = 18;

5. there is no right answer.

Question 4: Is it possible to solve the system of equations of the matrix method, if the determinant of the system is zero?

1. yes;

2. No;

3. always;

4. occasionally;

5. there is no right answer.

Question 5. What is the determinant of the second order?

1.;

2;

3;

4;

5. there is no right answer.

Task 7.

Question 1. How to record expansion in the unit vectors of the vector joining the points A (3, 5, 7) and B (5, 9, 12)?

1.;

2;

3;

4;

5.

Question 2. When the vector and collinear?

1 when = 0;

2. When = 0;

3. The dot product of these vectors is 0;

4. When = ;

5. there is no right answer.

Question 3. In which case the vector called linearly independent?

1. If they - collinear;

2. if the equality = 0 is possible only when 1 = 2 = ... = 0;

3. possibly, if at least one of the coefficients 1, ... k 0;

4. zero;

5. there is no right answer.

Question 4. Which expression is called a linear combination of the vectors?

1. a = 0;

2. =

3. a = (c, d)

4 a-c = d

5. no right answer

Question 5: Can the four vectors in the plane to be linearly independent?

1. yes;

2. always;

3. sometimes;

4. there is no right answer.

5. No.

Task 8

Question 1. Can four vectors in three-dimensional space to be linearly independent?

1. yes;

2. No;

3. always;

4. occasionally;

5. there is no right answer.

Question 2. Are the vectors of vectors coplanar?

1. no;

2. Yes;

3. always;

4. occasionally;

5. No answer.

Question 3. Whether the vector product and lie in the plane formed by these vectors, if it is not equal to zero?

1. yes;

2. always;

3. sometimes;

4. there is no right answer.

5. No.

Question 4: What will change in the vector product, if you change the order of the multiplied vectors?

1. The order of the components (coordinates) of the vector-product;

2. The signs of the components of the vector-product;

3. module multiplies the sine of the angle between the vectors;

4. The length of the vector result;

5. there is no right answer.

Question 5. What can you say about the coordinates of the vectors, and if they are collinear?

1. they are equal to zero;

2. proportional to their coordinates;

3. they are positive;

4. they are negative;

5. there is no right answer.

Task 9

Question 1. The mixed product of a vector or scalar (ie, the number)?

Question 2. The scalar product - the number or vector?

Question 3. The vector product - the number or vector?

Question 4: What is the unit (length) and the vector product?

Question 5: What is the unit of the mixed produc