Question

If a matrix has 15 elements, how many possible orders can it have?

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Answer 1

Let the number of rows be m and the number of columns be n.

If the order of a matrix is m $\times$ n then the matrix has mn elements.

Given that mn = 15

m = 1, n = 15

m = 3, n = 5

m = 5, n = 3

m = 15, n = 1

Therefore the possible orders of the matrix are 1$\times$15, 3$\times$5, 5$\times$3, 15$\times$1

Therefore the number of possible orders is 4.