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

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If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

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6. If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

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7. Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

Let A = [a i] be required 3 x3 matrix
where a,ij , = 2 i – 3 j
∴ a₁₁, = 2–3 = –1. a₁₂ = 2–6 = 4. a₁₃,= 2–9 = 7
a₂₁ = 4 — 3 = 1. a₂₂ = 4 — 6 = —2 . a₂₃ = 4 –9 = 5
a₃₁ = 6 – 3 = 3, = 6 – 6 = 0 , a₃₃ = 6 – 9 = –3

$therefore space space space space space straight A equals open square brackets table row cell negative 1 end cell cell negative 4 end cell cell negative 7 end cell row 1 cell negative 2 end cell cell negative 5 end cell row 3 0 cell negative 3 end cell end table close square brackets$