Advertisements
Advertisements
प्रश्न
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is ______.
विकल्प
m × m
n × n
n × m
m × n
उत्तर
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is m × n.
Explanation:
Order of matrix A = m × n
Let order of matrix B be K × P
Order of matrix B' = P × K
If AB' is defined then the order of AB' is m × K if n = P
If B'A is defined then order of B'A is P × n when K = m
Now, order of B' = P × K
∴ Order of B = K × P
= m × n .....[∵ K = m, P = n]
APPEARS IN
संबंधित प्रश्न
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
The order of the matrix
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
Write the number of elements,
If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
Construct a 2 × 2 matrix, A = [aij], whose element is given by `a_(ij) = (i+j)^2/2`
Construct a 2 × 2 matrix, `A = [a_(ij)]` whose elements are given by `a_(ij) = (1 + 2j)^2/2`
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 1/2 |-3i + j|`
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 2i - j`
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is ______.
Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively.
The restrictions on n, k and p so that PY + WY will be defined are ______.
Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k respectively.
If n = p, then the order of the matrix is 7X - 5Z is ______.
If A, B are symmetric matrices of same order, then AB − BA is a ______.
Find matrix A such that `((2,-1),(1,0),(-3,4))A = ((-1, -8),(1, -2),(9,22))`
If a matrix has 5 elements, write all possible orders it can have.
Construct a matrix A = [aij]2×2 whose elements aij are given by aij = e2ix sin jx.
In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: The order of the matrix A
Construct a2 × 2 matrix where aij = `("i" - 2"j")^2/2`
The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is ____________.
`[(2,0,3),(5,1,0),(0,1,-1)]`
`[(0,-1,1),(2,-3,4),(3,-3,4)]`
The order of the single matrix obtained from `[(1,-1),(0,2),(2,3)] {[(-1,0,2),(2,0,1)] - [(0,1,23),(1,0,21)]}` is ____________.
Given that matrices A and B are of order 3 × n and m × 5 respectively, then the order of matrix C = 5A + 3B is:
If a matrix has 6 elements, then number of possible orders of the matrix can be ____________.
Consider the following information regarding the number of men and women workers in three factories I, II and III
| MEN WORKERS | WOMEN WORKERS | |
| I | 30 | 25 |
| II | 25 | 31 |
| III | 27 | 26 |
Which of the following represent the above information in the form of a 3 × 2 matrix.
If a matrix has 8 elements, what are the possible order it can have?
The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to ______.
