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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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