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Question
Construct a 2 × 2 matrix, A = [aij], whose element is given by `a_(ij) = (i+j)^2/2`
Solution
In general, a 2 × 2 matrix is given by `A = [(a_(11), a_(12)),(a_(21),a_22)]`
`a_ij = (i + j)^2/2`; i, j = 1, 2
`:. a_(11) = (1+1)^2/2 = 4/2 = 2`
`a_(12) = (1+2)^2/2 = 9/2`
`a_(21) = (2+1)^2/2 = 9/2`
`a_(22) = (2+2)^2/2`
`= 16/2`
= 8
Therefore, the required matrix is A = `[(2, 9/2), (9/2 , 8)]`
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