Construct a 2 x 3 matrix whose elements are given by aij. = i +

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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 .

Here a_ij = 2 i - j
$therefore$ a_{11 = 2 (1) - 2 = 2 - 1 = 1,}a₁₂ = 2 (1) - 2 = 2 - 2 = 0
a_{13 = 2 (1) - 3 = 2 - 3 = - 1,}a₁₄ = 2 (1) - 4 = 2 - 4 = - 2
a_{21 = 2 (2) - 1 = 4 - 1 = 3,}a₂₂ = 2 (2) - 2 = 4 - 2 = 2
a_{23 = 2 (2) - 3 = 4 - 3 = 1,}a₂₄ = 2 (2) - 4 = 4 - 4 = 0

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

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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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