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Class 12 Tuition > Learn Exercise 3.1 > If a matrix has 18 elements, what are the possible...
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If a matrix has 18 elements, what are the possible orders it can have? What, if ithas 5 elements?

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18= 1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3 Therefore, there are 6 posiible orders. And for 5 it is 1 X 5 and 5 X 1, So, it has 2 possible orders
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BSc Math(H), MBA(Finance)

For 18 elements1×18,2×9,3×6,6×3,9×2,18×1. & for 5 elements1×5,5×1.Factors of total no of elements are orders
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If a matrix has 18 elements. The possible orders it can have are, 1 X 18 18 X 1 2 X 9 9 X 2 3 X 6 6 X 3 If a matrix has 5 elements, then the possible order will be either 1 X 5 or 5 X 1
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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 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18. The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3) Hence,...
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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 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18. The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3) Hence, the possible orders of a matrix having 18 elements are: 1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3 (1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5. Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1. read less
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Related Questions

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?
24 = 1 X 24 = 2 X 12 = 3 X 8 = 4 X 6 = 6 X 4 = 8 X 3 = 12 X 2 = 24 X 1 So, there are 8 orders possible. Similarly 13 = 1 X 13 and 13 X1, So, only 2 orders are possible.
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