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Matrices

Short Answer Type

11. Construct a 3 x 4 matrix whose elements are

a_{i j} = i.j

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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

Let A = [a_{i j} ] be required 3x4 matrix where a_ij-= 2 i – j
$therefore$ a₁₁ = 2 - 1 = 1,   a₁₂ = 2 - 2 = 0,   a₁₃ = 2 - 3 = - 1,
a₁₄ = 2 - 4 = - 2
  a₂₁ = 4 - 1 = 3, a₂₂ = 4 - 2 = 2, a₂₃ = 4 - 3 = 1,
  a₂₄ = 4 - 4 = 0,
a₃₁ = 6 - 1 = 5,   a₃₂ = 6 - 2 = 4, a₃₃ = 6 - 3 = 3,
a₃₄ = 6 - 4 = 2

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