Algebra and geometry
Date: 2015-10-07; view: 654.
Вопрос № 1
1 Let 
, 
be vectors in 
. Find the angle between these vectors.
2 0;
Вопрос № 2
Let , 
be vectors in . Find the angle between these vectors .
2 
;
Вопрос № 3
Let 
, 
be vector in . Find the angle between these vectors.
2 
;
Вопрос № 4
Let 
, 
be vectors in . Find the angle between these vectors
0;
Вопрос № 5
Let 
, 
be vectors in 
. Find the angle between these vectors.
0;
Вопрос № 6
Let 
, 
be vectors in . Find the angle between these vectors.
0;
Вопрос № 7
Let 
, 
be vectors in . Find the angle between these vectors..
;
Вопрос № 8
Let 
, 
be vectors in . Find the angle between these vectors.
;
.
Вопрос № 9
9) Let 
and 
be vectors in 
such that 
. Find 
if: 
.
2;
Вопрос № 10
Let and be vectors in such that . Find if: 
.
-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 -6
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 
.
$$2
Вопрос № 103
$$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 .
$$2 
Вопрос № 109
$$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 center is the origin and major axis vertices: 
, eccentricity: 
.
$$2 
Вопрос № 159
$$1 Find the standard-form equation of the ellipse if it's center is the origin and the focus: 
, corresponding directrix: 
.
$$2 
Вопрос № 160
$$1 Find the standard-form equation of the ellipse if it's center is the origin and the focus: 
, corresponding directrix: 
.
$$2 
Вопрос № 161
$$1 The equation of the ellipse is 
. Find foci.
$$2 
Вопрос № 162
$$1 The equation of the ellipse is . Find foci.
$$2
Вопрос № 163
$$1 The equation of the ellipse is . Find the eccentricity.
$$2 
Вопрос № 164
$$1 The equation of the ellipse is . Find the eccentricity.
$$2 
Вопрос № 165
$$1 Put the equation 
in standard form and find foci.
$$2 
Вопрос № 166
$$1 Put the equation 
in standard form and find foci.
$$2 
Вопрос № 167
$$1 Put the equation 
in standard form and find foci.
$$2 
Вопрос № 168
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its foci: , asymptotes : 
.
$$2 
Вопрос № 169
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its foci: , asymptotes: 
.
$$2 
Вопрос № 170
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its foci: 
, eccentricity: 
.
$$2 
Вопрос № 171
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its foci: 
, eccentricity: 
.
$$2 
Вопрос № 172
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its major axis vertices: 
, eccentricity: .
$$2 
Вопрос № 173
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its major axis vertices: 
, eccentricity: 
.
$$2 
Вопрос № 174
$$1 Find the standard-form equation of the hyperbola if its center is the origin and its major axis vertices: 
, asymptotes: 
.
$$2 
Вопрос № 175
$$1 Find the standard-form equation of the parabola if the parabola is symmetric about x-axis and passed through the origin and the point 
.
$$2 
Вопрос № 176
$$1 Find the standard-form equation of the parabola if the parabola is symmetric about y-axis, the focus is the point and the vertex is the origin.
$$2 
Вопрос № 177
$$1 Find the standard-form equation of the parabola if the parabola is symmetric about y-axis and passed through the origin and the point 
.
$$2 
Вопрос № 178
$$1 Find points of intersection of the parabola 
and the straight line 
.
$$2 
Вопрос № 179
$$1 Find the standard-form equation of the parabola if the parabola is symmetric about x-axis and passed through the origin and the point .
$$2 
Вопрос № 180
$$1 Find the standard-form equation of the parabola if the parabola is symmetric about x-axis and passed through the origin and the point 
.
$$2 
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