Construct a 3 x 4 matrix whose elements areai j = i.j from Mat

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Matrices

Short Answer Type

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11. 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 = 1, a₁₂ =1 . 2 = 2, a₁₃ = 1 . 3 = 3, a₁₄ = 1 . 4 = 4
a₂₁ = 2 . 1 = 2, a₂₂ =2 . 2 = 4, a₂₃= 2 . 3 = 6, a₂₄ = 2 . 4 = 8
a₃₁ = 3 . 1 = 3, a₃₂ =3 . 2 = 6, a₃₃= 3 . 3 = 9, a₃₄ = 3 . 4 = 12

$therefore space space space straight A equals open square brackets table row 1 2 3 4 row 2 4 6 8 row 3 6 9 12 end table close square brackets$

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12. Construct a 2 x 3 matrix whose elements are given by a_ij. = i + 2 j .

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13. Construct a 2 x 3 matrix whose elements are given by a_ij. = i + 2 j .

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14. Construct a 2 x 2 matrix, A = [a_{i j}], whose elements are given by :

straight a subscript ij equals fraction numerator left parenthesis straight i plus straight j right parenthesis squared over denominator 2 end fraction

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15. Construct a 2 x 2 matrix, A = [a_{i j}], whose elements are given by :

straight a subscript ij equals i over j

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16. Construct a 2 x 2 matrix, A = [a_{i j}], whose elements are given by :

straight a subscript ij equals fraction numerator left parenthesis straight i plus 2 space straight j right parenthesis squared over denominator 2 end fraction

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17. Construct a 3 X 2 matrix whose elements are given by

straight a subscript ij equals 1 half left square bracket straight i minus 3 space straight j right square bracket

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18. Construct a 3 x 4 matrix, whose elements are given by :

straight a subscript ij equals 1 half open vertical bar negative 3 straight i plus straight j close vertical bar

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19. Construct a 3 x 4 matrix, whose elements are given by :

a_ij = 2 i - j

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20. If

open square brackets table row cell straight x minus 2 straight y end cell cell negative straight y end cell row cell 3 straight x end cell 4 end table close square brackets equals open square brackets table row cell negative 4 end cell 3 row 6 4 end table close square brackets

find the values of .x and y.

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