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:
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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