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Algebra and geometry

Вопрос № 1

$$1 Let , be vectors in . Find the angle between these vectors.

$$2 0;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 2

$$1 Let , be vectors in . Find the angle between these vectors .

$$2 ;

$$3 ;

$$4 ;

$$5 0;

$$6 .

 

 

Вопрос № 3

$$1 Let , be vector in . Find the angle between these vectors.

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 0.

 

 

Вопрос № 4

$$1 Let , be vectors in . Find the angle between these vectors

$$2 0;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 5

$$1 Let , be vectors in . Find the angle between these vectors.

$$2 0;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 6

$$1 Let , be vectors in . Find the angle between these vectors.

$$2 0;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 7

$$1 Let , be vectors in . Find the angle between these vectors..

$$2 ;

$$3 ;

$$4 ;

$$5 0;

 

$$6 .

 

 

Вопрос № 8

$$1 Let , be vectors in . Find the angle between these vectors.

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 9

$$1 9) Let and be vectors in such that . Find if: .

$$2 2;

$$3 5;

$$4 1;

$$5 15;

$$6 0.

 

Вопрос № 10

$$1 Let and be vectors in such that . Find if: .

$$2 -1;

$$3

$$4

$$5

$$6

 

 

Вопрос № 11

$$1 Let and be vectors in such that . Find if: .

$$2 12;

$$3

$$4

$$5

$$6

 

 

Вопрос № 12

$$1 Let and be vectors in such that . Find if: .

$$2 ;

$$3

$$4

$$5

$$6

 

 

Вопрос № 13

$$1 Let and be vectors in such that . Find if: .

$$2 ;

$$3

$$4

$$5

$$6

 

Вопрос № 14

$$1 Let and be vectors in such that . Find the angle between and if: .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 15

$$1 Let and be vectors in such that . Find the angle between and if: .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 16

$$1 Determine so that vectors and are orthogonal, where .

$$2 ;

$$3

$$4

$$5

$$6

 

Вопрос № 17

$$1 Determine so that vectors and are orthogonal, where .

$$2 -6

 

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 18

$$1 Determine so that vectors and are orthogonal, where .

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 19

$$1 Determine so that vectors and are orthogonal, where .

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 20

$$1 Determine so that vectors and are orthogonal, where .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 21

$$1 Find and if .

$$2

$$3

$$4

$$5



$$6

 

 

Вопрос № 22

$$1 Find and if .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 23

$$1 Find and if .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 24

$$1 Find and if .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 25

$$1 Find and if .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 26

$$1 Solve the system .

$$2

$$3

$$4

$$5

$$6 No solution.

 

Вопрос № 27

$$1 Solve the system .

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 28

$$1 Solve the system .

$$2 No solution;

$$3

$$4

$$5

$$6

 

Вопрос № 29

$$1 Solve the system .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 30

$$1 Solve the system .

$$2 No solution;

$$3

$$4

$$5

$$6

 

Вопрос № 31

$$1 Solve the system .

$$2

$$3 No solution;

$$4

$$5

$$6

 

Вопрос № 32

$$1 Determine so that the system has the unique solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 33

$$1 Determine so that the system has the unique solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 34

$$1 Determine so that the system has the unique solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 35

$$1 Determine so that the system has the unique solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 36

$$1 Determine so that the system has the unique solution.

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 37

$$1 Determine so that the system has more the one solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 38

$$1 Determine so that the system has more then one solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 39

$$1 Determine so that the system has more then one solution.

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 40

$$1 $$1 Determine so that the system has more then one solution.

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 41

$$1 Determine so that the system has more then one solution.

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 42

$$1 Let . Find .

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 43

 

$$1 Let . Find .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 44

 

$$1 Let . Find .

$$2 does not exist;

$$3

$$4

$$5

$$6

 

Вопрос № 45

$$1 Let , . Find

$$2

$$3

$$4

$$5

$$6 .

 

 

Вопрос № 46

$$1 Let , . Find

$$2

$$3 s

$$4

$$5

$$6 .

 

 

Вопрос № 47

$$1 Let , . Find

$$2

$$3

$$4

$$5

$$6 .

 

Вопрос № 48

 

$$1 Given . Find a vector such that .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 49

$$1 Given . Find a vector such that .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 50

 

$$1 Given . Find a vector such that .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 51

$$1 Write the vector as a linear combination of the vectors .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 52

$$1 Write the vector as a linear combination of the vectors .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 53

 

$$1 Write the vector as a linear combination of the vectors .

$$2

$$3

$$4

$$5

$$6

 

 

Вопрос № 54

$$1 Write the vector as a linear combination of the vectors .

$$2

$$3

$$4

$$5

$$6

 

Вопрос № 55

$$1 Write as a linear combination of matrices

.

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 56

$$1 Write as a linear combination of matrices

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 57

$$1 Write as a linear combination of matrices

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 58

 

Write as a linear combination of matrices

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 59

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 60

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4

$$5

$$6

 

 

Вопрос № 61

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 62

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5

$$6 .

 

Вопрос № 63

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 64

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 65

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 66

$$1 Find the rank of matrix .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 67

$$1 Find a dimension of the solution space of the homogeneous system

.

$$2

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 68

$$1 Find a dimension of the solution space of the homogeneous system

.

$$2

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 69

$$1 $$1 Find a dimension of the solution space of the homogeneous system

.

$$2

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

$$1 Find a dimension of the solution space of the homogeneous system

.

$$2

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

 

Вопрос № 70

$$1 Find a dimension of the solution space of the homogeneous system

.

$$2

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 71

$$1 Find a dimension of the subspace of generated by vectors .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

Вопрос № 72

$$1 Find a dimension of the subspace of generated by vectors .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 73

$$1 Find a dimension of the subspace of generated by vectors .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 74

$$1 Find a dimension of the subspace of generated by vectors .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 75

$$1 Find a dimension of the subspace of generated by vectors , .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 76

$$1 Let be linear operators on defined by . Find .

$$2 ;

$$3 ;

$$4 ;

$$5 ;

$$6 .

 

Вопрос № 77

$$1 Let be linear operators on defined by . Find


Date: 2015-12-11; view: 496


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