Linear algebra test with answers 75 questions

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Linear algebra test, 75 questions.


Task 1


Question 1. What is the dimension of the vector a = (2, 3, 4, 5):


1. 1

2. 2

3. 3

4. 4

5. 5.


2. For Q vectors a = (1, 2, 3) and a = (4, 5, 6) the vector c = 2a + 3b is:


1.,

2.,

3.,

4.,

5. The operation is not defined.


Question 3. vectors a = (1, 2, 3) and a = (4, 5, 6,8) the vector c = 2a + 3b is:


6.,

7.,

8.,

9.,

10. The operation is not defined.




Question 4. Are the vectors a = (1,2,5), and = (2,4,10) are linearly dependent?

Question 5. What value of the parameter and the vectors e = (2,3) and c = (4a) are orthogonal?



Task 2


Question 1. Calculate the scalar product:

Question 2. Calculate the scalar product:

Question 3. Calculate the scalar product:

Question 4. The system of n vectors is called a basis of Rn

if the vectors of this system:

Question 5. Euclidean space is a linear (vector) space, which defines:

Activity 3


A = B = C =


Question 1. 3A + 2B =:

Question 2 2A-3B =

Question 3. A + AT =:

Question 4. BT + CT =:

Question 5. Addition of matrices determined if the matrix:

Task 4


A = B = C =



Question 1. AB =:


1.,

2.,

3.,

4.,

5.


Question 2 AB + C =:


1.,

2.,

3.,

4.,

5.,



Question 3. AB + BC =:


1.,

2.,

3.,

4.,

5.


Question 4: AE =:


1. A

2. E

3. EA

4. Not determined.

5. arbitrary value.


Q5 = A0:


1. A

2. 0

3. E

4. Not determined.

5. arbitrary value.




Task 5

Calculate the value of the determinant


Question 1.


1. 10,

2. 9,

3. 8

4. 7,

5. 0.


Question 2.


1. 10,

2. 8

3. 0

4. 5,

5. 4.



Question 3.




1. 10,

2. 8

3. 5,

4. 4

5. 0.


Question 4.


1. 0

2. 20

3. 12

4. 34

5. 5.


Question 5.


1. 16

2. 14

3. 20

4. 0

5. 1.


Task 6



To determine the rank.


Question 1.


1. 1

2. 2

3. 3

4. 4

5. 5.


Question 2.


1. 1

2. 2

3. 3

4. 4

5. 5


Question 3.


1. 1

2. 2

3. 3

4. 4

5. 5


Question 4.


1. 1

2. 2

3. 3

4. 4

5. 5.


Question 5.


1. 1

2. 2

3. 3

4. 4

5. 5.


Task 7


Question 1. The Matrix, for which there is no inverse matrix, called:


1. degenerate

2. Normally,

3. symmetric

4. Accession,

5. Union.



Question 2. Select a true statement;


1.,

2.

3. The characteristics are not comparable.



Question 3. Select the true statement:


1.,

2.,

3. The characteristics are not comparable.



Question 4. The determinant is defined for matrices:


1. arbitrary,

2. square,

3. attached,

4. symmetrical,

5. neotritsattelnyh.



Question 5. Rank of the matrix is \u200b\u200bequal to the maximum number;


1 linearly independent rows,

2. linearly independent columns,

3. rows

4. columns

5. The values \u200b\u200bof the elements of the matrix.



Task 8


Question 1. The augmented matrix of the system is as follows


Describe her decision:


1. Joint determined,

2. joint, unspecified,

3. uncertain.



Question 2. The augmented matrix of the system is as follows:



Describe her decision:


1. Joint determined,

2. joint, unspecified,

3. uncertain.



Question 3: The augmented matrix of the system is as follows:

Additional information

Question 4. The augmented matrix of the system is as follows:


Describe her decision:



1. joint, opedelennaya,

2. joint, unspecified,

3. uncertain.







Question 5. augmented matrix of issue 4 define the maximum number of basic solutions:


1. 1

2. 2

3. 3

4. 4

5. 5.



Task 9

Extended matrix system has the form




Question 1.


1. 1

2. 2

3. 3

4. 4

5. 5.

Question 2.


1. -1

2. -2

3. -3

4. -4

5. -6.






Question 3.


1. 1

2. 2

3. 3

4. 4

5. 5.



Question 4.


1.- 1

2. 2

3. 3

4. 4

5. 5.


Question 5.


1. 1

2. 2

3. 3

4. 4

5. 5.




Task 10


Question 1: The reference is the solution in which all the free variables:


1. positive

2. negative

3. Indeed,

4. zero,

5. arbitrary.


Question 2. The basic solution is a support program if it is:


1. The non-negative,

2. The non-positive,

3. Indeed,

4. integer,

5. random.


Question 3: The number of variables is bazasnyh;


1. rank of the augmented matrix,

2. The number of variables,

3. The number of equations,

4. set arbitrarily,

5. The number of free variables.


Question 4: What is the difference between the number of basic and free variables for the system:




1. 1

2. 2

3. 3

4. 4

5. 5.


Question 5. What is the difference between the number of basic and free variables for the system:




1. 1

2. 2

3. 3

4. 4

5. 5.




Task 11


Question 1. The system is called homogeneous, if the free terms:

1. equal to zero,

2. have an arbitrary value,

3. positive

4. The negative

5. integer.


Question 2. The homogeneous system always:


1. The Joint,

2. inconsistent,

3. Determine

4. undefined,

5. there.


Question 3. The equation is called:


1. characteristic,

2. revealing,

3. symmetric

4. The operator,

5. fundamental.


Question 4. If the problem has three eigenvalues, eigenvectors as it has:


1. 1

2. 2

3. 3

4. 4

5. 5.


Question 5. The problem of the linear model of trade is bezdifitsitnoy if the property value is:


1. 1

2. 2

3. 3

4. 4

5. 5.



Activity 12




Question 1. For the quadratic form matrix is \u200b\u200bas follows:

Question 2. The quadratic form is called uncertain if it:

Question 3. If the quadratic form is called:

Question 4. If the quadratic form is called:

Question 5. To determine the constant sign of the quadratic form used criteria:


Activity 13

Question 1. Matrix uravnenieAX = B has a solution in a general form:

Question 2. The matrix equation XA = B has a solution in a general form:

Question 3. The matrix equation AXB = C has a solution in the form of obschschem:

Question 4: The matrix equation X + AX \u200b\u200b= Y has a solution in a general form:

Question 5. The matrix equation 5X + AX \u200b\u200b= Y has a solution in a general form:

Activity 14


Question 1. Coordinates the middle segment are as follows;

Question 2. The equation of a straight line with a slope is:

Question 3. The equation of the line passing through a given point in a given direction is as follows:


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