Question:
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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To find the possible orders of a matrix with a given number of elements, factorize the total number of elements and pair the factors.
Updated On: Jan 16, 2025
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The Correct Option is D
Solution and Explanation
The total number of elements in a matrix is given by the product of its rows (\(m\)) and columns (\(n\)), i.e., \(m \times n = 36\).
The possible orders (\(m, n\)) of the matrix are all pairs of positive integers whose product equals 36.
The factors of 36 are: \[ 1, 2, 3, 4, 6, 9, 12, 18, 36. \]
The possible pairs \((m, n)\) are: \[ (1, 36), (36, 1), (2, 18), (18, 2), (3, 12), (12, 3), (4, 9), (9, 4), (6, 6). \] Thus, there are 9 possible orders for the matrix.
The factors of 36 are: \[ 1, 2, 3, 4, 6, 9, 12, 18, 36. \]
The possible pairs \((m, n)\) are: \[ (1, 36), (36, 1), (2, 18), (18, 2), (3, 12), (12, 3), (4, 9), (9, 4), (6, 6). \] Thus, there are 9 possible orders for the matrix.
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