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Algebra and geometry

Вопрос № 1

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

$$2 0;

Вопрос № 2

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

$$2 ;

Вопрос № 3

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

$$2 ;

Вопрос № 4

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

$$2 0;

Вопрос № 5

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

$$2 0;

Вопрос № 6

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

$$2 0;

Вопрос № 7

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

$$2 ;

Вопрос № 8

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

$$2 ;

Вопрос № 9

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

$$2 2;

Вопрос № 10

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

$$2 -1;

Вопрос № 11

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

$$2 12;

Вопрос № 12

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

$$2 ;

Вопрос № 13

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

$$2 ;

Вопрос № 14

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

$$2 ;

Вопрос № 15

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

$$2 ;

Вопрос № 16

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

$$2 ;

Вопрос № 17

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

$$2

Вопрос № 18

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

$$2

Вопрос № 19

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

$$2

Вопрос № 20

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

$$2

Вопрос № 21

$$1 Find and if .

$$2

 



Вопрос № 22

$$1 Find and if .

$$2

Вопрос № 23

$$1 Find and if .

$$2

Вопрос № 24

$$1 Find and if .

$$2

Вопрос № 25

$$1 Find and if .

$$2

Вопрос № 26

$$1 Solve the system .

$$2

 



Вопрос № 27

$$1 Solve the system .

$$2

 



Вопрос № 28

$$1 Solve the system .

$$2 No solution;

Вопрос № 29

$$1 Solve the system .

$$2

Вопрос № 30

$$1 Solve the system .

$$2 No solution;

Вопрос № 31

$$1 Solve the system .

$$2

Вопрос № 32

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

$$2

Вопрос № 33

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

$$2

Вопрос № 34

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

$$2

Вопрос № 35

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

$$2

Вопрос № 36

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

$$2

 



Вопрос № 37

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

$$2

Вопрос № 38

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

$$2

Вопрос № 39

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

$$2

 



Вопрос № 40

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

$$2

 



Вопрос № 41

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

$$2

Вопрос № 42

$$1 Let . Find .

$$2

 



 



Вопрос № 43

 



$$1 Let . Find .

$$2

Вопрос № 44

 



$$1 Let . Find .

$$2 does not exist;

Вопрос № 45

$$1 Let , . Find

$$2

 



Вопрос № 46

$$1 Let , . Find

$$2

 



Вопрос № 47

$$1 Let , . Find

$$2

Вопрос № 48

 



$$1 Given . Find a vector such that .

$$2 ;

Вопрос № 49

$$1 Given . Find a vector such that .

$$2 ;

Вопрос № 50

 



$$1 Given . Find a vector such that .

$$2 ;

 



Вопрос № 51

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

$$2

Вопрос № 52

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

$$2

Вопрос № 53

 



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

$$2

Вопрос № 54

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

$$2

Вопрос № 55

$$1 Write as a linear combination of matrices

.

$$2 ;

 



Вопрос № 56

$$1 Write as a linear combination of matrices

$$2 ;

Вопрос № 57

$$1 Write as a linear combination of matrices

$$2 ;

Вопрос № 58

 



Write as a linear combination of matrices

$$2 ;

Вопрос № 59

$$1 Find the rank of matrix .

$$2 ;

 



Вопрос № 60

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 61

$$1 Find the rank of matrix .

$$2 ;

 



Вопрос № 62

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 63

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 64

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 65

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 66

$$1 Find the rank of matrix .

$$2 ;

Вопрос № 67

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

.

$$2

Вопрос № 68

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

.

$$2

Вопрос № 69

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

.

$$2

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

.

$$2

 



 



Вопрос № 70

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

.

$$2

 



Вопрос № 71

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

$$2 ;

Вопрос № 72

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

$$2 ;

 



Вопрос № 73

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

$$2 ;

Вопрос № 74

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

$$2 ;

Вопрос № 75

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

$$2 ;

Вопрос № 76

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

$$2 ;

Вопрос № 77

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

$$2 ;

Вопрос № 78

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

$$2 ;

Вопрос № 79

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

$$2 ;

Вопрос № 80

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

$$2 ;

Вопрос № 81

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

$$2 ;

 



Вопрос № 82

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

$$2 ;

 



Вопрос № 83

$$1 Which of the following mappings are linear?

$$2 ;

 



Вопрос № 84

$$1 Which of the following mappings are linear?

$$2 ;

 



Вопрос № 85

$$1 Which of the following mappings are linear?

$$2 ;

Вопрос № 86

$$1 Find the matrix of the linear operator on defined by with respect to the usual basis.

$$2 ;

 



Вопрос № 87

$$1 Find the matrix of the linear operator on defined by with respect to the usual basis.

$$2 ;

Вопрос № 88

$$1 Find the matrix of the linear operator on defined by with respect to the usual basis.

$$2 ;

Вопрос № 89

$$1 Find the matrix of the linear operator on defined by with respect to the usual basis.

$$2 ;

Вопрос № 90

$$1 Find the matrix of the linear operator on defined by with respect to the usual basis.

$$2 ;

Вопрос № 91

$$1 Let be the linear operator on defined by . Find .

$$2

Вопрос № 92

$$1 Let be the linear operator on defined by . Find .

$$2

 



Вопрос № 93

$$1 Let be the linear operator on defined by . Find .

$$2

 



Вопрос № 94

$$1 Let be the linear operator on defined by . Find .

$$2

 



 



Вопрос № 95

$$1 Let be the linear operator on defined by . Find .

$$2

 



Вопрос № 96

$$1 Let be the linear operator on defined by . Find .

$$2

 



Вопрос № 97

$$1 For the matrix , find the cofactor of the entry .

$$2

 



Вопрос № 98

$$1 For the matrix , find the cofactor of the entry .

$$2

 



 



Вопрос № 99

$$1 For the matrix , find the cofactor of the entry .

$$2

 



Вопрос № 100

$$1 Evaluate the determinant of the matrix .

$$2

 



Вопрос № 101

$$1 Evaluate the determinant of the matrix .

$$2

Вопрос № 102

$$1 Evaluate the determinant of the matrix .

$$2

$$3

$$4

$$5

$$6

 



Вопрос № 103

$$1 Evaluate the determinant of the matrix .

$$2

 



Вопрос № 104

$$1 Evaluate the determinant of the matrix .

$$2

 



 



Вопрос № 105

$$1 Let . Find .

$$2

 



Вопрос № 106

$$1 Let . Find .

$$2

 



 



Вопрос № 107

$$1 Let . Find .

$$2

 



Вопрос № 108

$$1 Let . Find .

$$2

$$3

 



 



Вопрос № 109

$$1 Let . Find .

$$2 Does not exist;

 



Вопрос № 110

$$1 Let . Find .

$$2 Does not exist;

 



Вопрос № 111

$$1 Let be the linear operator on defined by .Find .

$$2

 



Вопрос № 112

$$1 Let be the linear operator on defined by .Find .

$$2

 



 



Вопрос № 113

$$1 Let be the linear operator on defined by . Find .

$$2

 



 



Вопрос № 114

$$1 Let be the linear operator on defined by .Find .

$$2

 



Вопрос № 115

$$1 Let be the linear operator on defined by . Find .

$$2

 



 



Вопрос № 116

$$1 Find all eigenvalues of the matrix .

$$2

 



Вопрос № 117

$$1 Find all eigenvalues of the matrix .

$$2

 



 



Вопрос № 118

$$1 Find all eigenvalues of the matrix .

$$2

 



 



Вопрос № 119

$$1 Find all eigenvalues of the matrix .

$$2 Does not exist;

 



 



Вопрос № 120

$$1 Find all eigenvalues of the matrix .

$$2

 



 



Вопрос № 121

$$1 Find the slope and the segment cut out on the y-axis of the straight line .

$$2

 



Вопрос № 122

$$1 Find the slope and the segment cut out on the y-axis of the straight line .

$$2

 



Вопрос № 123

$$1 Find the slope and the segment cut out on the y-axis of the straight line .

$$2 .

 



Вопрос № 124

$$1 Find the equation of the straight line that passes through the origin and is parallel to the straight line ;

$$2

 



Вопрос № 125

$$1 Find the equation of the straight line that passes through the origin and is parallel to the straight line ;

$$2 ;

 



Вопрос № 126

$$1 Find the equation of the straight line that passes through the point and is parallel to the straight line .

$$2 ;

 



Вопрос № 127

$$1 Find the equation of the straight line that passes through the point and is parallel to the straight line .

$$2 ;

 



 



Вопрос № 128

. $$1 Find the equation of the straight line that passes through the point and is perpendicular to the straight line .

$$2 ;

 



Вопрос № 129

$$1 Find the equation of the straight line that passes through the point and is perpendicular to the straight line .

$$2 ;

 



Вопрос № 130

$$1 Find the equation of the straight line that passes through the point and is perpendicular to the straight line .

$$2 ;

 



Вопрос № 131

$$1 Find the equation of the straight line that passes through the point and is perpendicular to the straight line .

$$2 ;

 



Вопрос № 132

$$1 Find the equation of the straight line that passes through points and .

$$2 ;

Вопрос № 133

$$1 Find the equation of the straight line that passes through points and .

$$2 ;

 



Вопрос № 134

$$1 Find the equation of the straight line that passes through points and .

$$2 ;

Вопрос № 135

$$1 Find the equation of the straight line that passes through points and .

$$2 ;

Вопрос № 136

$$1 Find the equation of the straight line if it passes through the point and the angle between it and the x-axis is equal to .

$$2 ;

 



Вопрос № 137

$$1 Find the equation of the straight line if it passes through the point and the angle between it and the x-axis is equal to .

$$2 ;

 



Вопрос № 138

$$1 Find the equation of the straight line if it passes through the point and the angle between it and the x-axis is equal to .

$$2 ;

 



Вопрос № 139

$$1 Find the equation of the straight line if it passes through the point and the angle between it and the x-axis is equal to .

$$2 ;

 



Вопрос № 140

$$1 Find the angle between straight lines , .

$$2 ;

Вопрос № 141

$$1 Find the angle between straight lines , .

$$2 ;

 



Вопрос № 142

$$1 Find the angle between straight lines , .

$$2 ;

 



Вопрос № 143

$$1 Find the angle between straight lines , .

$$2 ;

Вопрос № 144

$$1 Find the angle between straight lines and .

$$2 ;

 



Вопрос № 145

$$1 Find the angle between straight lines and .

$$2 ;

 



 



Вопрос № 146

$$1 Find the angle between straight lines and .

$$2 ;

 



Вопрос № 147

 



$$1 Find the distance between the straight line and the point

$$2

Вопрос № 148

$$1 Find the distance between the straight line and the point .

$$2

 



Вопрос № 149

$$1 Find the distance between the straight line and the point .

$$2

 



 



Вопрос № 150

$$1 Find the distance between the straight line and the point

$$2

 



Вопрос № 151

$$1 Put the equation in standard form and find foci.

$$2

 



Вопрос № 152

$$1 Put the equation in standard form and find foci.

$$2

 



Вопрос № 153

$$1 Put the equation in standard form and find foci.

$$2

 



Вопрос № 154

$$1 Find the standard-form equation of the ellipse if it’s center is the origin and foci: , major axis vertices: .

$$2

 



Вопрос № 155

$$1 Find the standard-form equation of the ellipse if it’s center is the origin and foci: , eccentricity: .

$$2

 



Вопрос № 156

$$1 Find the standard-form equation of the ellipse if it’s center is the origin and foci: , major axis vertices: .

$$2

 



Вопрос № 157

$$1 Find the standard-form equation of the ellipse if it’s center is the origin and major axis vertices: , eccentricity: .

$$2

 



Вопрос № 158

$$1 Find the standard-form equation of the ellipse if it’s cente


Date: 2015-12-11; view: 489


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