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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

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8. Construct a 3 x 4 matrix whose elements are

a_{i j} = i +J

Let A = [ a_ii] be required 3 x 4 matrix where a_ij= i + j
_{$therefore space space space$}a₁₁ = 1 + 1 = 2, a₁₂ =1+2, a₁₃=1 + 3 = 4, a₁₄ = 1 + 4 = 5
a₂₁ = 1 + 1 = 2, a₂₂ =1+2, a₂₃=1 + 3 = 4, a₂₄ = 1 + 4 = 6
a₃₁ = 1 + 1 = 2, a₃₂ =1+2, a₃₃=1 + 3 = 4, a₃₄ = 1 + 4 = 7