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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

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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.

We are given that $open square brackets table row cell straight x minus 2 straight y end cell cell negative straight y end cell row cell 3 straight x end cell 4 end table close square brackets equals open square brackets table row cell negative 4 end cell 3 row 6 4 end table close square brackets$

From the definition of equality of matrices, we have
x + 2y= 4    ...(1)
– y = 3    ...(2)
3 x = 6    ...(3)
From (2).    y = –3
From (3),    x = 2
Also (1) is satisfied for x = 2, y = – 3 we have x = 2, y = – 3

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Previous Year Papers

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Short Answer Type

20. If find the values of .x and y.