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Matrices

Question
CBSEENMA12032870

Construct a 2 x 2 matrix, A = [ai 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

Solution

A = [ aij ] is 2 x 2 matrix where straight a subscript ij equals fraction numerator left parenthesis straight i plus 2 space straight j right parenthesis squared over denominator 2 end fraction
therefore space space straight a subscript 11 equals fraction numerator left parenthesis 1 plus 2 right parenthesis squared over denominator 2 end fraction equals 9 over 2 comma space space space space space space space space space space space space space space space space straight a subscript 12 equals fraction numerator left parenthesis 1 plus 4 right parenthesis squared over denominator 2 end fraction equals 25 over 2
space space space space space straight a subscript 21 equals fraction numerator left parenthesis 2 plus 2 right parenthesis cubed over denominator 2 end fraction equals 16 over 2 equals 8 space space space space space space space space space space space straight a subscript 22 equals fraction numerator left parenthesis 2 plus 4 right parenthesis squared over denominator 2 end fraction equals 36 over 2 equals 18
therefore space space space space space straight A equals open square brackets table row cell 9 over 2 end cell cell 25 over 2 end cell row 8 18 end table close square brackets