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Matrices

Short Answer Type

Consider the following information regarding the number of men and women workers in three factories I. II and III

	Men Workers	Women Workers
I	30	25
II	25	31
III	27	26

Represent the above information in the form of a 3 x 2 matrix. What does the entry in the third row and second column represent ?

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In the matrix $straight A equals open square brackets table row 2 5 19 cell negative 7 end cell row 35 cell negative 2 end cell cell 5 over 12 end cell 12 row cell square root of 5 end cell 1 cell negative 5 end cell 17 end table close square brackets. space Write$

(i) The order of the matrix
(ii) The number of elements,
(iii) Write the elements a₁₃,a₂₁ a₃₃ a₂₄’ a₂₃

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If a matrix has 8 elements, what arc the possible orders it can have ?

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4.
If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

We know that a matrix of order m x n has mn elements. Therefore, for finding all possible orders of a matrix with 24 elements, w e will find all ordered pairs with products of elements as 24.
∴ all possible ordered pairs are
(1, 24), (24. 1), (2, 12), (12. 2). (3, 8), (8, 3), (4. 6), (6, 4)
∴ possible orders are
1 x 24. 24 x 1, 2 x 12, 12 x 2, 3 x 8, 8 x 3, 4 x 6. 6 x 4
If number of elements =13, then possible orders are 1 x 13, 13 x l.

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