Question:medium
If a matrix has 36 elements, the number of possible orders it can have is:
If a matrix has 36 elements, the number of possible orders it can have is:
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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: Feb 25, 2026
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The Correct Option is D
Solution and Explanation
The total count of elements in a matrix is the result of multiplying its row count by its column count:
\[m \times n = 36,\]
where \( m \) represents the number of rows and \( n \) represents the number of columns.
To identify the matrix's potential dimensions, list all pairs of positive integers \( (m, n) \) whose product is \( 36 \). 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, indicating \( 9 \) distinct matrix dimensions. Therefore, the number of possible dimensions is (D) 9.
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