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Question
Construct a 2 × 2 matrix A = [aij] whose elements aij are given by \[a_{ij} = \begin{cases}\frac{\left| - 3i + j \right|}{2} & , if i \neq j \\ \left( i + j \right)^2 & , if i = j\end{cases}\]
Solution
\[a_{11} = \left( 1 + 1 \right)^2 = 4\]
\[ a_{12} = \frac{\left| - 3 \times 1 + 2 \right|}{2} = \frac{1}{2}\]
\[ a_{21} = \frac{\left| - 3 \times 2 + 1 \right|}{2} = \frac{5}{2}\]
\[ a_{22} = \left( 2 + 2 \right)^2 = 16\]
\[\text{Hence, the matrix A} = \begin{bmatrix}4 & \frac{1}{2} \\ \frac{5}{2} & 16\end{bmatrix} .\]
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