Linear algebra test

Collection of test items

Task 1

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

eleven,
eleven,
eleven,
eleven,
5. 5.

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

one. ,
one. ,
one. ,
one. ,
5. the operation is undefined.

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

one. ,
one. ,
one. ,
one. ,
10. the operation is undefined.



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

1.are,
2. are not,
3. it is impossible to determine.








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

1.
2.
3.
4.
5. for any value.

Task 2

Question 1. Calculate the dot product of vectors:




eleven,
eleven,
eleven,
eleven,
5. the operation is undefined.


Question 2. Calculate the dot product of vectors:




1 26,
2 27,
3 28,
4 29,
5 operation is undefined.

Question 3. Calculate the dot product of vectors:




eleven,
eleven,
eleven,
eleven,
5. the operation is undefined.


Question 4. A system of n vectors is called a basis of the space Rn
if the vectors of this system:

1.linearly dependent,
2.linearly independent,
3.positive,
4.negative,
5. arbitrary.


Question 5. Euclidean space is a linear (vector) space in which it is defined:

1.dot product,
2.vector product,
3.mixed work,
4.vector length,
5. vector direction.









Task 3

A = B = C =

Question 1A + 3B =:

one. ,
one. ,
one. ,
one. ,
one. .

Question 2. 2A-3B =

one. ,
one. ,
one. ,
one. ,
5.

Question 3. A + AT =:

one. ,
one. ,
one. ,
one. ,
5.

Question 4. BT + CT =:

one. ,
one. ,
one. ,
one. ,
5.


Question 5. Matrix addition is defined if matrices:

1.signed,
2. valid,
3.reasonable,
4.have the same dimension,
5. have an arbitrary dimension.


Task 4

A = B = C =


Question 1. AB =:

one. ,
one. ,
one. ,
one. ,
5.

Question 2. AB + C =:

one. ,
one. ,
one. ,
one. ,
one. ,


Question 3. AB + BC =:

one. ,
one. ,
one. ,
one. ,
5.

Question 4. AE =:

1.A,
2.E,
3. EA,
4.not defined,
5. arbitrary value.

Question 5. A0 =:

1.A,
eleven,
3.E,
4.not defined,
5. arbitrary value.



Task 5
Calculate Determinant Values

Question 1.

eleven,
eleven,
eleven,
eleven,
5. 0.

Question 2.

eleven,
eleven,
eleven,
eleven,
5. 4.


Question 3.



eleven,
eleven,
eleven,
eleven,
5. 0.

Question 4.

eleven,
eleven,
eleven,
eleven,
5. 5.

Question 5.

eleven,
eleven,
eleven,
eleven,
5. 1.

Task 6


Determine the rank of the matrix.

Question 1.

eleven,
eleven,
eleven,
eleven,
5. 5.

Question 2.

eleven,
eleven,
eleven,
eleven,
5 5

Question 3.

eleven,
eleven,
eleven,
eleven,
5 5

Question 4.

eleven,
eleven,
eleven,
eleven,
5. 5.

Question 5.

eleven,
eleven,
eleven,
eleven,
5. 5.

Task 7

Question 1. A matrix for which there is no inverse matrix is ​​called:

1.degenerate,
2.normal,
3.symmetrical,
4.attached,
5.Allied.


Question 2. Choose the correct statement;

one. ,
2.
3. characteristics are not comparable.


Question 3. Choose the correct statement:

one. ,
one. ,
3. The characteristics are not comparable.


Question 4. The determinant is given for matrices:

1. arbitrary,
2.square,