Question:

If a matrix has 36 elements, the number of possible orders it can have is:

Show Hint

The number of possible orders of a matrix with \( n \) elements is equal to the number of factor pairs of \( n \). Each pair \( (m, n) \) represents a valid order where \( m \times n = n \).
Updated On: Jan 18, 2025
  • 13
  • 3
  • 5
  • 9
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

The total number of elements in a matrix is given by the product of its number of rows and columns: \[ m \times n = 36, \] where \( m \) is the number of rows, and \( n \) is the number of columns. To determine the possible orders of the matrix, find all pairs of positive integers \( (m, n) \) such that their product equals \( 36 \). These pairs are the factors of \( 36 \): \[ (1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), (18, 2), (36, 1). \] There are \( 9 \) such pairs, corresponding to \( 9 \) possible orders of the matrix. Hence, the number of possible orders is (D) 9.
Was this answer helpful?
0
0