Question

If a matrix has 32 elements. what is the possible orders it can have?​

Answer 1

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$\huge \underline \bold \red {Explanation:}$

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 24 elements, we have to find all the ordered pairs of natural numbers whose product is 24.

The ordered pairs are(1,24),(24,1),(2,12),(12,2),(3,8),(8,3),(4,6) and (6,4)

Hence, the possible orders of a matrix having 24 elements are:

1×24,24×1,2×12,12×2,3×8,8×3,4×6,6×4

(1,13) and (13,1) are the ordered pairs of natural numbers whose product is 13.

Hence, the possible orders of a matrix having 13 elements are 1×13 and 13×1