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For what real value of y will matrix A be equal to matrix B, where
- a)11, 3
- b)No real value
- c)1/3, 1/2
- d)2 and 3
Correct answer is option 'B'. Can you explain this answer?
For what real value of y will matrix A be equal to matrix B, where
a)
11, 3
b)
No real value
c)
1/3, 1/2
d)
2 and 3
|
Mihir Yadav answered |
⇒ y2 - 4y = -3
⇒ y2 - 4y + 3 = 0
⇒ y2 -3y - y +3 = 0
⇒ y (y - 3) -1 (y-3) = 0
⇒(y - 1) (y - 3) = 0
⇒ y = 1,3
But these are not real numbers.
We have another equation:
⇒ 5y = 6y2 + 1
⇒ 6y2 -5y +1 = 0
⇒ 6y2 -3y - 2y + 1 = 0
⇒ 3y (2y - 1) - 1 (2y - 1) = 0
⇒ (3y - 1) (2y - 1) = 0
⇒ y = 1/2, 1/3
Hence value of y is 1/2, 1/3
the value of a22 is
- a)0
- b)-2
- c)2
- d)None
Correct answer is option 'C'. Can you explain this answer?
the value of a22 isa)
0
b)
-2
c)
2
d)
None
|
Amrit Raj answered |
I=2,j=2
modulus of 2-6=4
4/2=2
hence the correct ans is C :2
If the order of matrix A is m×p. And the order of B is p×n. Then the order of matrix AB is?- a)n × p
- b)m × n
- c)n × p
- d)n × m
Correct answer is option 'D'. Can you explain this answer?
If the order of matrix A is m×p. And the order of B is p×n. Then the order of matrix AB is?
a)
n × p
b)
m × n
c)
n × p
d)
n × m
|
Suresh Iyer answered |
If we are given 2 matrices of with order a×b and c×d, in order to be multiplicable, b must be equal to c and the resultant matrix will have order a×d. So using this formula in this question, We have p = p and so the resultant matrix will have m×n order. So, order of matrix AB is m×n.
is example of- a)an identity matrix
- b)a zero matrix.
- c)a Scalar m
- d)diagonal matrix.
Correct answer is option 'D'. Can you explain this answer?
is example ofa)
an identity matrix
b)
a zero matrix.
c)
a Scalar m
d)
diagonal matrix.
|
Raj Raunak answered |
Diagonal matrix is a matrix in which the entries outside the main diagonalare all zero.
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
a)
b)
c)
d)
|
Sushil Kumar answered |
P(n) : An = {(1+2n, -4n), (n,(1 - 2n))}
= P(k + 1) = {(1+2(k+1), -4(k+1)), (k+1, (1 - 2(k+1)}
= {(1+2k+2, -4k-4) (k+1, 1-2k-2)}
= {(2k+3, -4k-4), (k+1, -2k-1)}
= P(k + 1) = {(1+2(k+1), -4(k+1)), (k+1, (1 - 2(k+1)}
= {(1+2k+2, -4k-4) (k+1, 1-2k-2)}
= {(2k+3, -4k-4), (k+1, -2k-1)}
Then the value of x is ____- a)6
- b)3
- c)2
- d)0
Correct answer is option 'B'. Can you explain this answer?
Then the value of x is ____a)
6
b)
3
c)
2
d)
0
|
Geetika Shah answered |
= x+10 = 3x+4
= x = 3
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A- a)Equivalent
- b)Inverse
- c)Adjoint
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A
a)
Equivalent
b)
Inverse
c)
Adjoint
d)
none of the above
|
Rajesh Gupta answered |
ANSWER :- a
Solution :- Matrix equivalence is an equivalence relation on the space of rectangular matrices.
For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions
- The matrices can be transformed into one another by a combination of elementary row and column operations.
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be equivalent of A.
If A, B are symmetric matrices of same order then the matrix AB-BA is a- a)Skew-symmetric matrix
- b)Skew-Harmitian matrix
- c)Symmetric matrix
- d)Harmitian matrix
Correct answer is option 'A'. Can you explain this answer?
If A, B are symmetric matrices of same order then the matrix AB-BA is a
a)
Skew-symmetric matrix
b)
Skew-Harmitian matrix
c)
Symmetric matrix
d)
Harmitian matrix
|
|
Sushil Kumar answered |
A and B are symmetric matrices, therefore, we have:
A′=A and B′=B..........(i)
Consider
(AB−BA)′=(AB)′ − (BA)′,[∵(A−B)′=A′B′]
=B′A′− A′B',[∵(AB)′= B′A]
=BA−AB [by (i) ]
=−(AB−BA)
∴(AB−BA) ′=−(AB−BA)
Thus, (AB−BA) is a skew-symmetric matrix.
A′=A and B′=B..........(i)
Consider
(AB−BA)′=(AB)′ − (BA)′,[∵(A−B)′=A′B′]
=B′A′− A′B',[∵(AB)′= B′A]
=BA−AB [by (i) ]
=−(AB−BA)
∴(AB−BA) ′=−(AB−BA)
Thus, (AB−BA) is a skew-symmetric matrix.
Which of the following is a nilpotent matrix- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a nilpotent matrix
a)
b)
c)
d)
|
|
Sushil Kumar answered |
An n×n matrix A is called nilpotent if Ak=O, where O is the n×n zero matrix.
(a) The matrix A is nilpotent if and only if all the eigenvalues of A is zero.
(b) The matrix A is nilpotent if and only if An=O.
Therefore, option c gives zero matrix.
(a) The matrix A is nilpotent if and only if all the eigenvalues of A is zero.
(b) The matrix A is nilpotent if and only if An=O.
Therefore, option c gives zero matrix.
If 
and 
, then AB=?- a)[7]
- b)[1 - 12]
- c)
- d)[18]
Correct answer is option 'A'. Can you explain this answer?
If and , then AB=?
and , then AB=?a)
[7]
b)
[1 - 12]
c)
d)
[18]
|
Ritu Singh answered |
A = [2, 3, 4]
Therefore AXB = {(2*1) + (3*(-1)) + (4*2)}
AXB = {2 + (-3) + 8}
AXB = 7
Therefore AXB = {(2*1) + (3*(-1)) + (4*2)}AXB = {2 + (-3) + 8}
AXB = 7
The system of the linear equations x + y – z = 6, x + 2y – 3z = 14 and 2x + 5y – λz = 9 (λ ∈ R) has a unique solution if- a)λ = -8
- b)λ = 8
- c)λ = -7
- d)λ = 7
Correct answer is option 'B'. Can you explain this answer?
The system of the linear equations x + y – z = 6, x + 2y – 3z = 14 and 2x + 5y – λz = 9 (λ ∈ R) has a unique solution if
a)
λ = -8
b)
λ = 8
c)
λ = -7
d)
λ = 7
|
Vaishnavi Kanera answered |
For a solution to be unique the value of the determinant of the solution should not be equal to 0
then x is equal to- a) –1
- b)2
- c)1
- d)No value of x
Correct answer is option 'A'. Can you explain this answer?
then x is equal toa)
–1
b)
2
c)
1
d)
No value of x
|
Sonålí Raåz answered |
If u solve this matrix by addition of matrix then u get x^2+ x. x-1 -x +4. x +2 matrix which is equal to matrix. 0. -2 5. 1 ..........so now by equality of matrix , equalte any of four equation with the corresponding element of second matrix ....i.e, (-x +4)= 5 which gives the value of x equal to -1 ...Ans.
The inverse of 
is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
The inverse of is
isa)
b)
c)
d)
|
Adarsh Gupta answered |
A11=0A12=1A21=1A22=0A^-1=[01] [10]
For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:
- a)det(A) = 9
- b)det(A) = 81
- c)det(A) = 7
- d)det(A) = 4
Correct answer is option 'C'. Can you explain this answer?
For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:
a)
det(A) = 9
b)
det(A) = 81
c)
det(A) = 7
d)
det(A) = 4
|
Aniket Dasgupta answered |
Skew Symmetric Even Ordered Matrix and Determinant
Skew Symmetric Matrix:
A skew symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, if A is a skew symmetric matrix, then A^T = -A.
Example:
[0 -3 4]
[3 0 -5]
[-4 5 0]
This is a 3x3 skew symmetric matrix because A^T = -A.
Even Ordered Matrix:
An even ordered matrix is a square matrix whose order is even. In other words, if A is an even ordered matrix, then the order of A is 2n, where n is a positive integer.
Example:
[2 1 5 3]
[4 6 8 2]
[9 7 1 5]
[3 4 2 6]
This is a 4x4 even ordered matrix because the order of A is 2n=4.
Determinant of a Skew Symmetric Even Ordered Matrix:
The determinant of a skew symmetric even ordered matrix is always equal to zero. This is because the determinant of a skew symmetric matrix of odd order is always equal to zero and the determinant of any even ordered matrix can be expressed as a sum of permutations of the determinants of its n x n submatrices. Since the submatrices of a skew symmetric matrix are also skew symmetric, their determinants are equal to zero. Therefore, the determinant of a skew symmetric even ordered matrix is also equal to zero.
Solution:
a) det(A) = 9
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'a' is not true.
b) det(A) = 81
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'b' is not true.
c) det(A) = 7
This statement is false because the determinant of a skew symmetric even ordered matrix is always equal to zero.
d) det(A) = 4
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'd' is not true.
Therefore, the correct answer is option 'c'.
Skew Symmetric Matrix:
A skew symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, if A is a skew symmetric matrix, then A^T = -A.
Example:
[0 -3 4]
[3 0 -5]
[-4 5 0]
This is a 3x3 skew symmetric matrix because A^T = -A.
Even Ordered Matrix:
An even ordered matrix is a square matrix whose order is even. In other words, if A is an even ordered matrix, then the order of A is 2n, where n is a positive integer.
Example:
[2 1 5 3]
[4 6 8 2]
[9 7 1 5]
[3 4 2 6]
This is a 4x4 even ordered matrix because the order of A is 2n=4.
Determinant of a Skew Symmetric Even Ordered Matrix:
The determinant of a skew symmetric even ordered matrix is always equal to zero. This is because the determinant of a skew symmetric matrix of odd order is always equal to zero and the determinant of any even ordered matrix can be expressed as a sum of permutations of the determinants of its n x n submatrices. Since the submatrices of a skew symmetric matrix are also skew symmetric, their determinants are equal to zero. Therefore, the determinant of a skew symmetric even ordered matrix is also equal to zero.
Solution:
a) det(A) = 9
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'a' is not true.
b) det(A) = 81
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'b' is not true.
c) det(A) = 7
This statement is false because the determinant of a skew symmetric even ordered matrix is always equal to zero.
d) det(A) = 4
Since the determinant of a skew symmetric even ordered matrix is always equal to zero, this statement is false. Therefore, option 'd' is not true.
Therefore, the correct answer is option 'c'.
The value of λ, for which system of equations. x + y + z = 1, x + 2y + 2z = 3, x + 2y + λz = 4, have no solution is
- a)1
- b)2
- c)0
- d)3
Correct answer is option 'B'. Can you explain this answer?
The value of λ, for which system of equations. x + y + z = 1, x + 2y + 2z = 3, x + 2y + λz = 4, have no solution is
a)
1
b)
2
c)
0
d)
3
|
|
Kiran Sengupta answered |
This question is unclear as there is no context or information provided. Please provide more details for me to give a relevant answer.
The inverse of 
is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
The inverse of is
isa)
b)
c)
d)
|
Hansa Sharma answered |
A = IA
AA-1 = I
A = {(1,0),(-1,1)}
A-1{(1,0),(-1,1)} = {(1,0),(0,1)}
R2 ----> R2 + R1
A^-1 {(1,0),(0,1)} = {(1,0),(1,1)}
I A-1 = {(1,0),(1,1)}
Therefore, A-1 = {(1,0),(1,1)}
AA-1 = I
A = {(1,0),(-1,1)}
A-1{(1,0),(-1,1)} = {(1,0),(0,1)}
R2 ----> R2 + R1
A^-1 {(1,0),(0,1)} = {(1,0),(1,1)}
I A-1 = {(1,0),(1,1)}
Therefore, A-1 = {(1,0),(1,1)}
The product of two matrics 
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
The product of two matrics
a)
b)
c)
d)
|
|
Sushil Kumar answered |
{(1*0, 2*2, 0*x) (2*0, 0*2, 1*x) (1*0, 0*2, 2*x)}
= {4, x, 2x}
= {4, x, 2x}
Consider the following information regarding the number of men and women workers in three BPOs I, II and III
What does the entry in the second row and first column represent if the information is represented as a 3 x 2 matrix?- a)The number of Men in BPO II
- b)The number of Women in BPO II
- c)The number of Women in BPO I
- d)The number of Men in BPO I
Correct answer is 'A'. Can you explain this answer?
Consider the following information regarding the number of men and women workers in three BPOs I, II and III
What does the entry in the second row and first column represent if the information is represented as a 3 x 2 matrix?
a)
The number of Men in BPO II
b)
The number of Women in BPO II
c)
The number of Women in BPO I
d)
The number of Men in BPO I
|
Sanjeevini Angadi answered |
The number of all possible matrices of order 3×3 with each entry 0 if 1 is- a)81
- b)512
- c)18
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The number of all possible matrices of order 3×3 with each entry 0 if 1 is
a)
81
b)
512
c)
18
d)
none of these
|
Harsh Majumdar answered |
To find the number of all possible matrices of order 3, we need to consider the number of choices for each entry in the matrix.
In a matrix of order 3, there are 9 entries. Each entry can be chosen from any number in the set {0, 1, 2, ..., 9} since there are no restrictions mentioned. Therefore, there are 10 choices for each entry.
Since each entry can be chosen independently, we can use the multiplication principle to find the total number of matrices. This principle states that if there are n choices for one event and m choices for another event, then there are n * m choices for both events together.
Applying this principle to our matrix, we have 10 choices for each of the 9 entries. Therefore, the total number of possible matrices of order 3 is 10^9.
Hence, the number of all possible matrices of order 3 is 10^9.
In a matrix of order 3, there are 9 entries. Each entry can be chosen from any number in the set {0, 1, 2, ..., 9} since there are no restrictions mentioned. Therefore, there are 10 choices for each entry.
Since each entry can be chosen independently, we can use the multiplication principle to find the total number of matrices. This principle states that if there are n choices for one event and m choices for another event, then there are n * m choices for both events together.
Applying this principle to our matrix, we have 10 choices for each of the 9 entries. Therefore, the total number of possible matrices of order 3 is 10^9.
Hence, the number of all possible matrices of order 3 is 10^9.
If 
, then 
is equal to - a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
If , then is equal to
, then is equal to a)
b)
c)
d)
|
|
Geetika Shah answered |
A’ = {(1,-1,5) (0,0,2)} B = {(-2,0) (0,2) (3,4)}
B’ = {(-2,0,3) (0,2,4)}
2B’ = 2{(-2,0,3) (0,2,4)}
2B’ = {(-4,0,6) (0,4,8)}
(A’ - 2B’) = {(1,-1,5) (0,0,2)} - {(-4,0,6) (0,4,8)}
= {(5,-1,-1) (0,-4,-6)}
(A’ - 2B’)’ = {(5,0) (-1,-4) (-1,-6)}
B’ = {(-2,0,3) (0,2,4)}
2B’ = 2{(-2,0,3) (0,2,4)}
2B’ = {(-4,0,6) (0,4,8)}
(A’ - 2B’) = {(1,-1,5) (0,0,2)} - {(-4,0,6) (0,4,8)}
= {(5,-1,-1) (0,-4,-6)}
(A’ - 2B’)’ = {(5,0) (-1,-4) (-1,-6)}
the value of a22 is- a)0
- b)-2
- c)2
- d)4
Correct answer is 'D'. Can you explain this answer?
the value of a22 isa)
0
b)
-2
c)
2
d)
4
|
Arpita Nair answered |
aij = 1/2 |i-3j|
As aij = a22 ie i = 2 and j = 2
By substituting the values in the equation, we get
a22 = 1/2 |2-3(2)| = 1/2 |-4| = 2
As aij = a22 ie i = 2 and j = 2
By substituting the values in the equation, we get
a22 = 1/2 |2-3(2)| = 1/2 |-4| = 2
The number of different orders of a matrix having 12 elements is- a)3
- b)1
- c)6
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The number of different orders of a matrix having 12 elements is
a)
3
b)
1
c)
6
d)
None of these
|
Nandini Iyer answered |
(1,12),(2,6),(3,4(,(4,3),(6,2),(12,1)
6 different matrices.
6 different matrices.
If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be true
- a)A and B are both null matrices
- b)Either of A is or B is a null matrix
- c)Either of them may be a zero matrix
- d)It is Not necessary that A = 0 or B = 0
Correct answer is option 'D'. Can you explain this answer?
If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following can be true
a)
A and B are both null matrices
b)
Either of A is or B is a null matrix
c)
Either of them may be a zero matrix
d)
It is Not necessary that A = 0 or B = 0
|
|
Gaurav Kumar answered |
AB = 0 does not necessarily imply that either A or B is a null matrix
- Both matrices need not be null matrices.
- Both matrices need not be null matrices.
If A and B are square matrices of the same order, then(A+B)2 = A2+2AB+B2 implies- a)AB + BA = O
- b)AB = O
- c)AB = BA
- d)none of these.
Correct answer is 'A'. Can you explain this answer?
If A and B are square matrices of the same order, then(A+B)2 = A2+2AB+B2 implies
a)
AB + BA = O
b)
AB = O
c)
AB = BA
d)
none of these.
|
Samridhi Bajaj answered |
If A and B are square matrices of same order , then , product of the matrices is not commutative.Therefore , the given result is true only when AB = BA.
Which of the following property of matrix multiplication is correct:- a)Multiplication is not commutative in genral
- b)Multiplication is associative
- c)Multiplication is distributive over addition
- d)All of the mentioned
Correct answer is option 'D'. Can you explain this answer?
Which of the following property of matrix multiplication is correct:
a)
Multiplication is not commutative in genral
b)
Multiplication is associative
c)
Multiplication is distributive over addition
d)
All of the mentioned
|
Prasenjit Dasgupta answered |
Matrix multiplication is associative, distributive, but not commutative.
A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for- a)I < j
- b)I = j
- c)I > j
- d)I ≠ j
Correct answer is option 'D'. Can you explain this answer?
A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for
a)
I < j
b)
I = j
c)
I > j
d)
I ≠ j
|
|
Hansa Sharma answered |
In a diagonal matrix all elements except diagonal elements are zero.i.e.
If 
and 
then 
is equal to- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
If and then is equal to
and then is equal toa)
b)
c)
d)
|
Sakshi Dagar answered |
Hey multiply A by B . Then you easily get answer
What is the element in the 2nd row and 1st column of a 2 x 2 Matrix A = [ aij], such that a = (i + 3) (j – 1)- a)0
- b)4
- c)-5
- d)5
Correct answer is 'A'. Can you explain this answer?
What is the element in the 2nd row and 1st column of a 2 x 2 Matrix A = [ aij], such that a = (i + 3) (j – 1)
a)
0
b)
4
c)
-5
d)
5
|
Nishanth Joshi answered |
The element in the 2nd row and 1st column of the matrix A can be found by substituting i=2 and j=1 into the expression a = (i 3) (j 2) and simplifying:
a = (2 - 3) (1 - 2) = (-1) (-1) = 1
Therefore, the element in the 2nd row and 1st column of the matrix A is 1.
a = (2 - 3) (1 - 2) = (-1) (-1) = 1
Therefore, the element in the 2nd row and 1st column of the matrix A is 1.
If the order of the matrix is m×n, then how many elements will there be in the matrix?- a)mn
- b)m2 n2
- c)mn2
- d)2mn
Correct answer is option 'A'. Can you explain this answer?
If the order of the matrix is m×n, then how many elements will there be in the matrix?
a)
mn
b)
m2 n2
c)
mn2
d)
2mn
|
|
Neha Sharma answered |
The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.
, then (A2)` is equal to
and 
, then AB = ?
, then (AB)` is equal to- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
, then (AB)` is equal toa)
b)
c)
d)
|
|
Vikas Kapoor answered |
A ={(1,2) (4,3)} B = {(3,2) (-1,1)}
AB= {[(1*3)+(2*(-1)) (1*2)+(2*1)] [(4*3)+(3 *(-1)) (4*2)+(3*1)]}
= {(1,4) (9,11)}
AB= {[(1*3)+(2*(-1)) (1*2)+(2*1)] [(4*3)+(3 *(-1)) (4*2)+(3*1)]}
= {(1,4) (9,11)}
For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:- a)det(A) = 9
- b)det(A) = 81
- c)det(A) = 0
- d)et(A) = 4
Correct answer is option 'C'. Can you explain this answer?
For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:
a)
det(A) = 9
b)
det(A) = 81
c)
det(A) = 0
d)
et(A) = 4
|
|
Raghav Bansal answered |
Determinant of a skew symmetric odd ordered matrix A is always 0 .
If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is- a)3×3
- b)4×1
- c)3×4
- d)1×4
Correct answer is option 'D'. Can you explain this answer?
If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is
a)
3×3
b)
4×1
c)
3×4
d)
1×4
|
|
Nandini Iyer answered |
In matrix 1*3 is one row and 3 columns and in 3*4 is three rows and four column hence multiplied matrix will be 1*4.
If A is square matrix of order 3, then the true statement is (where l is unit matrix).- a) Det (–A) = –det A
- b) Det A = 0
- c) Det (A + l) = 1 + det A
- d)Det 2A = 2 det A
Correct answer is option 'A'. Can you explain this answer?
If A is square matrix of order 3, then the true statement is (where l is unit matrix).
a)
Det (–A) = –det A
b)
Det A = 0
c)
Det (A + l) = 1 + det A
d)
Det 2A = 2 det A
|
|
Deepak Kumar answered |
A+l)=Det(A)+Det(l)
This statement is false.
The correct statement is: Det(A+l) = 1 + tr(A) + tr(A)^2, where tr(A) is the trace of matrix A (i.e. the sum of its diagonal elements).
This statement is false.
The correct statement is: Det(A+l) = 1 + tr(A) + tr(A)^2, where tr(A) is the trace of matrix A (i.e. the sum of its diagonal elements).
The inverse of a matrix is defined for- a)Only square matrices
- b)Diagonal matrices
- c)all matrices
- d)Rectangular matrices
Correct answer is option 'A'. Can you explain this answer?
The inverse of a matrix is defined for
a)
Only square matrices
b)
Diagonal matrices
c)
all matrices
d)
Rectangular matrices
|
Arun Khanna answered |
If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A−1. A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. ... For a noncommutative ring, the usual determinant is not defined.
If A and B are square matrices of order 2, then (A + B)2 equal to- a) A2 + 2 AB + B2
- b) A2 + AB + BA + B2
- c)A2 + 2BA + B2
- d) None of these
Correct answer is option 'B'. Can you explain this answer?
If A and B are square matrices of order 2, then (A + B)2 equal to
a)
A2 + 2 AB + B2
b)
A2 + AB + BA + B2
c)
A2 + 2BA + B2
d)
None of these
|
Manasa Das answered |
Solution:
Given, A and B are square matrices of order 2.
(A B)^2 = (A B) (A B)
Distributing the product, we get
(A B)^2 = A^2 B + A B^2 + A B^2 + B^2
(A B)^2 = A^2 B + 2 A B^2 + B^2
(A B)^2 = A (A B) B + B^2
(A B)^2 = A^2 B + A B B + B^2
(A B)^2 = A^2 B + A B^2 + B^2
Therefore, the correct option is (B).
Given, A and B are square matrices of order 2.
(A B)^2 = (A B) (A B)
Distributing the product, we get
(A B)^2 = A^2 B + A B^2 + A B^2 + B^2
(A B)^2 = A^2 B + 2 A B^2 + B^2
(A B)^2 = A (A B) B + B^2
(A B)^2 = A^2 B + A B B + B^2
(A B)^2 = A^2 B + A B^2 + B^2
Therefore, the correct option is (B).
- a)
- b)AB = [–2 –1 4]
- c)
- d)AB does not exist
Correct answer is option 'D'. Can you explain this answer?
a)
b)
AB = [–2 –1 4]
c)
d)
AB does not exist
|
Sonali answered |
A is 3×1 matrix whereas B is 3×3 matrix.so ,it does not exist
Let A and B be two non zero square matrics and AB and BA both are defined. It means- a)No. of columns of A ≠ No. of rows of B
- b)No. of rows of A ≠ No. of columns of B
- c)Both matrices (A) and (B) have same order
- d)Both matrices (A) and (B) does not have same order
Correct answer is option 'C'. Can you explain this answer?
Let A and B be two non zero square matrics and AB and BA both are defined. It means
a)
No. of columns of A ≠ No. of rows of B
b)
No. of rows of A ≠ No. of columns of B
c)
Both matrices (A) and (B) have same order
d)
Both matrices (A) and (B) does not have same order
|
Deepika Sen answered |
Must be equal to the number of rows of B.
b)No. of rows of A must be equal to the number of columns of B.
c)No. of rows of A must be equal to the number of rows of B.
d)No. of columns of A must be equal to the number of columns of B.
b)No. of rows of A must be equal to the number of columns of B.
c)No. of rows of A must be equal to the number of rows of B.
d)No. of columns of A must be equal to the number of columns of B.
If A is a skew – symmetric matrix, then trace of A is equal to- a)1
- b)–1
- c)0
- d)None of these
Correct answer is 'C'. Can you explain this answer?
If A is a skew – symmetric matrix, then trace of A is equal to
a)
1
b)
–1
c)
0
d)
None of these
|
|
Nandini Iyer answered |
We know that for a skew-symmetric matrix the sum of diagonal elements is zero.
a[ij] = 0∀i = j
So,tr(A) = 0
a[ij] = 0∀i = j
So,tr(A) = 0
For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5- a)0
- b)3
- c)-3
- d)1.
Correct answer is option 'B'. Can you explain this answer?
For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5
a)
0
b)
3
c)
-3
d)
1.
|
Shivani answered |
Find determinant of coefficients of the eqns given....and equal tht to zero....u ll get the ans...HOPE U GOT IT...
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