Advertisements
Advertisements
प्रश्न
If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
उत्तर
We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.
The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3)
Hence, the possible orders of a matrix having 18 elements are:
1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3
(1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5.
Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.
APPEARS IN
संबंधित प्रश्न
Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
If A is a 3 × 3 matrix |3A| = k|A|, then write the value of k.
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
Write the number of elements,
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
Write the elements a13, a21, a33, a24, a23
If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
Construct a 2 × 2 matrix, `A= [a_(ij)]`, whose elements are given by `a_(ij) = i/j`
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) = 2i - j`
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 ______.
Find matrix A such that `((2,-1),(1,0),(-3,4))A = ((-1, -8),(1, -2),(9,22))`
Find the value of k if M = `[(1,2),(2,3)]` and `M^2 - km - I_2 = 0`
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.
If A = `[(2, 3),(1, 2)]`, B = `[(1, 3, 2),(4, 3, 1)]`, C = `[(1),(2)]`, D = `[(4, 6, 8),(5, 7, 9)]`, then which of the sums A + B, B + C, C + D and B + D is defined?
Construct a2 × 2 matrix where aij = |–2i + 3j|
Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is ______.
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 ______.
The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is ____________.
The number of all the possible matrices of order 2 x 2 with each entry 0, 1, or 2 is ____________.
The order of [x y z] `[("a","h","g"),("h","b","f"),("g","f","c")] [("x"),("y"),("z")]` is ____________.
If A is an m x n matrix such that AB and BA are both defined, then B is a ____________.
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 ____________.
The order of set A is 3 and that of set B is 2. What is the number of relations from A to B?
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.
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 ______.
Let P = `[(1, 0, 0),(3, 1, 0),(9, 3, 1)]` and Q = [qij] be two 3 × 3 martices such that Q – P5 = I3. Then `(q_21 + q_31)/q_32` is equal to ______.
If A is a 2 × 3 matrix such that AB and AB' both are defined, then the order of the matrix B is ______.
