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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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Let A = [a_{i j} ) be required 3x2 matrix, where

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

straight a subscript 11 equals 1 half open vertical bar 1 minus 3 close vertical bar equals 1 half left parenthesis 2 right parenthesis equals 1 comma space space space straight a subscript 12 equals 1 half open vertical bar 1 minus 6 close vertical bar equals 1 half left parenthesis 5 right parenthesis equals 5 over 2 straight a subscript 21 equals 1 half open vertical bar 2 minus 3 close vertical bar equals 1 half left parenthesis 1 right parenthesis equals 1 half. space straight a subscript 22 equals 1 half open vertical bar 2 minus 6 close vertical bar equals 1 half left parenthesis 4 right parenthesis equals 2 straight a subscript 31 equals 1 half open vertical bar 3 minus 3 close vertical bar equals 1 half left parenthesis 0 right parenthesis equals 0 comma space space space space straight a subscript 32 equals 1 half open vertical bar 3 minus 6 close vertical bar equals 1 half left parenthesis 3 right parenthesis equals 3 over 2 straight A equals open square brackets table row 1 cell 5 over 2 end cell row cell 1 half end cell 2 row 0 cell 3 over 2 end cell end table close square brackets

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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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