Higher mathematics
Replenishment date: 01.02.2024
Contents: Higher Mathematics.pdf (125.73 KB)
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Description
The basis minor of a matrix is any non-zero minor whose order is equal to ... of the matrix
Response type: Text response
The vector a{4, −8, 11} has length equal to ... @3.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
√201
√202
√203
Distributivity (*) of multiplication on the right with respect to matrix addition looks like this: ...
Answer type: Single choice • with the choice of one correct answer from several proposed options
C*(A+B)=C*A+C*B
(A+B)*C=A*C+B*C
C*(AB)=C*AC*B
(AB)*C=A*CB*C
For the system of equations {3x₁ − x₂ = 1, 2x₁ + x₂ = 5, x₁ − 2x₂ = 0, establish a correspondence between the characteristics and their values: @1.png
Response Type: Mapping
A. Rank of the main matrix
B. Rank of the extended matrix
C. Number of solutions to the system
D 2
E.3
F. 0
If the vector a(3, −4, 5) is multiplied by the number 6, then the sum of the coordinates of the vector 6a will be equal to ... @6.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
25
24
26
If any row (column) of a matrix consists of only zeros, then its determinant is equal to...
Response type: Text response
If the equation of the plane is given by the point A(−2, 2, 8) and the normal n(1, 2, 3), then the coefficient of the variable y in this equation is equal to ... @3.png
Response type: Text response
If the elements of two rows (columns) of the matrix are ..., then the determinant is equal to zero
Response type: Text response
The coordinates of the middle of the segment with ends at points A(-3,-2,5) and A(5,2,1) are equal to ...
Answer type: Single choice • with the choice of one correct answer from several proposed options
(4,2,6)
(1,0,3)
(7,8,9)
Matrix A is called ... if its determinant is nonzero
Answer type: Single choice • with the choice of one correct answer from several proposed options
degenerate
inverse
non-degenerate
A matrix transposed twice is...
Answer type: Single choice • with the choice of one correct answer from several proposed options
inverse matrix
original matrix
transposed matrix
square of the transposed matrix
The minor of a matrix element coincides with the algebraic complement in the case when...
Answer type: Single choice • with the choice of one correct answer from several proposed options
(i + j) – odd number
(i + j) – even number
(i + j) = 1
The ordinate of the intersection point of the lines y1=2x+1 and y2=-2x+3 is ...
Response type: Text response
The transition from matrix A to a new matrix, in which the rows and columns have been swapped while maintaining order, is called ... matrix A
Response type: Text response
The product of matrices A = ((2, −5), (−3, 6), (4, 7)) and B = ((−3, 4), (5, −9)) is the matrix C equal to ... @ 3.png
Response Type: Sort
1 ((−7452, 9355), (7484, −9323))
2 ((1076, −1325), (−1060, 1341))
3 ((−148, 195), (156, −187))
4 ((24, −25), (−20, 29))
The product of matrices A = ((2, −5), (−3, 6), (4, 7)) and B = ((−3, 4), (5, −9)) is the matrix C equal to ... @ 4,1.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((31, −53), (−39, 66), (−23, 47))
((−31, 53), (39, −66), (23, −47))
((25, 66), (−17, 47), (31, −53))
((21, 35), (33, −66), (32, −47))
Let the vector a{−3, 7, 2} be given, then the length of the vector −4a is … @7.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
√992
√990
√989
Let a matrix A = ((3, −2), (−1, 5)) be given, then the second power of the matrix A (A²) is equal to ... @1.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((11, −16), (−8, 27))
((9, 4), (1, 25))
((−3, 2), (1, 5))
((9, −4), (1, 25))
Let a system of equations A = (2x₁ − 3x₂ + x₃ = 5, x₁ + x₂ − 3x₃ = 7, 5x₁ − x₂ + 6x₃ = 1) be given, then the determinant |A₁| of this system is … @4.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
142
143
144
Let a system of equations be given A = {2x₁ − 3x₂ + x₃ = 5, x₁ + x₂ − 3x₃ = 7, 5x₁ − x₂ + 6x₃ = 1, then the determinant
Response type: Text response
The vector a{4, −8, 11} has length equal to ... @3.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
√201
√202
√203
Distributivity (*) of multiplication on the right with respect to matrix addition looks like this: ...
Answer type: Single choice • with the choice of one correct answer from several proposed options
C*(A+B)=C*A+C*B
(A+B)*C=A*C+B*C
C*(AB)=C*AC*B
(AB)*C=A*CB*C
For the system of equations {3x₁ − x₂ = 1, 2x₁ + x₂ = 5, x₁ − 2x₂ = 0, establish a correspondence between the characteristics and their values: @1.png
Response Type: Mapping
A. Rank of the main matrix
B. Rank of the extended matrix
C. Number of solutions to the system
D 2
E.3
F. 0
If the vector a(3, −4, 5) is multiplied by the number 6, then the sum of the coordinates of the vector 6a will be equal to ... @6.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
25
24
26
If any row (column) of a matrix consists of only zeros, then its determinant is equal to...
Response type: Text response
If the equation of the plane is given by the point A(−2, 2, 8) and the normal n(1, 2, 3), then the coefficient of the variable y in this equation is equal to ... @3.png
Response type: Text response
If the elements of two rows (columns) of the matrix are ..., then the determinant is equal to zero
Response type: Text response
The coordinates of the middle of the segment with ends at points A(-3,-2,5) and A(5,2,1) are equal to ...
Answer type: Single choice • with the choice of one correct answer from several proposed options
(4,2,6)
(1,0,3)
(7,8,9)
Matrix A is called ... if its determinant is nonzero
Answer type: Single choice • with the choice of one correct answer from several proposed options
degenerate
inverse
non-degenerate
A matrix transposed twice is...
Answer type: Single choice • with the choice of one correct answer from several proposed options
inverse matrix
original matrix
transposed matrix
square of the transposed matrix
The minor of a matrix element coincides with the algebraic complement in the case when...
Answer type: Single choice • with the choice of one correct answer from several proposed options
(i + j) – odd number
(i + j) – even number
(i + j) = 1
The ordinate of the intersection point of the lines y1=2x+1 and y2=-2x+3 is ...
Response type: Text response
The transition from matrix A to a new matrix, in which the rows and columns have been swapped while maintaining order, is called ... matrix A
Response type: Text response
The product of matrices A = ((2, −5), (−3, 6), (4, 7)) and B = ((−3, 4), (5, −9)) is the matrix C equal to ... @ 3.png
Response Type: Sort
1 ((−7452, 9355), (7484, −9323))
2 ((1076, −1325), (−1060, 1341))
3 ((−148, 195), (156, −187))
4 ((24, −25), (−20, 29))
The product of matrices A = ((2, −5), (−3, 6), (4, 7)) and B = ((−3, 4), (5, −9)) is the matrix C equal to ... @ 4,1.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((31, −53), (−39, 66), (−23, 47))
((−31, 53), (39, −66), (23, −47))
((25, 66), (−17, 47), (31, −53))
((21, 35), (33, −66), (32, −47))
Let the vector a{−3, 7, 2} be given, then the length of the vector −4a is … @7.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
√992
√990
√989
Let a matrix A = ((3, −2), (−1, 5)) be given, then the second power of the matrix A (A²) is equal to ... @1.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((11, −16), (−8, 27))
((9, 4), (1, 25))
((−3, 2), (1, 5))
((9, −4), (1, 25))
Let a system of equations A = (2x₁ − 3x₂ + x₃ = 5, x₁ + x₂ − 3x₃ = 7, 5x₁ − x₂ + 6x₃ = 1) be given, then the determinant |A₁| of this system is … @4.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
142
143
144
Let a system of equations be given A = {2x₁ − 3x₂ + x₃ = 5, x₁ + x₂ − 3x₃ = 7, 5x₁ − x₂ + 6x₃ = 1, then the determinant
Additional Information
Let the vectors a{2, 3, 4} and b{5, 6, 7} be given, then the sum of the coordinates of the vector a + b is equal to ... @10.pngResponse type: Text response
The difference in coordinates of the normal vector of the plane 2x-y+3z-2=0 is ...
Response type: Text response
The difference between matrices A and B is called... matrices A with a matrix opposite to matrix B
Response type: Text response
The difference between the matrices A = ((7, −3), (2, 0)) and B = ((5, −2), (−3, 8)) is the matrix C, equal to ... @5.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((2, −1), (5, −8))
((2, 1), (5, 5))
((2, -5), (−5, 0))
((2, −8), (−1, 5))
Matrix rank under elementary transformations...
Answer type: Single choice • with the choice of one correct answer from several proposed options
is changing
does not change
decreases
increases
Place in the correct order the steps to solve the system of equations using the Gaussian method:
Response Type: Sort
1 create an extended matrix of the system
2, using elementary transformations, bring the extended matrix of the system to a stepwise form
3, based on the obtained step matrix, compose and solve a system of linear equations
Arrange the symbols for the relative position of the straight line l and the plane α in the order “the straight line intersects the plane, the straight line is perpendicular to the plane, the straight line is parallel to the plane”:
Response Type: Sort
1 l∩α
2 l ⊥ α
3 l ∥ α
Arrange the lines y1, y2 and y3 given by the equations in increasing order of their slopes:
Response Type: Sort
1 y₂=5
2 y₁=7x-2
3 y₃=-x+3
The distance from the point A(1, −4) to the line y = 4/3 ⋅ x − 4 is ... @7.png
Response type: Text response
The distance from point A(2,4,1) to the plane 2x-y+3z=2 is ...
Answer type: Single choice • with the choice of one correct answer from several proposed options
1/√14
2/√14
3/√15
The solution to the system of equations A = {2x₁ − 3x₂ + x₃ = 5, x₁ + x₂ − 3x₃ = 7, 5x₁ − x₂ + 6x₃ = 1 is ... @7.png
Answer type: Single choice • with the choice of one correct answer from several proposed options
((142/63), (−7/9), (−116/63))
((142/63), (−7/12), (−116/63))
((−142/63), (7/9), (−116/63))
A system of linear equations is called... a system of linear equations if all free terms in this system are equal to zero
Response type: Text response
The scalar product of the vectors a{2, 5, 7} and b{−3, 4, −9} is... @4.png
Response type: Text response
Match the minors of the matrix A = ((2, 3, 4), (5, −6, 7), (−8, 9, 0)) with their values: @3.png
Response Type: Mapping
A. M₁₂
B.M₂₁
C. M₃₂
D 56
E. -36
F. -6
The sum of the coordinates of the vector a = 2i + 3j − k is equal to ... @8.png
Response type: Text response
The sum of the coordinates of the normal vector of the plane 2x-y+3z-2=0 is ...
Response type: Text response