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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: 630

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