Question:
Construct a $2 \times 3$ matrix whose elements are $a_{i j}=\frac{(i-2 j)^{2}}{2}$.
Solution:
It is a (2 x 3) matrix. So, it has 2 rows and 3 columns.
Given $a_{i j}=\frac{(i-2 j)^{2}}{2}$
So, $a_{11}=\frac{1}{2}, a_{12}=\frac{9}{2}, a_{13}=\frac{25}{3}$
$a_{21}=0 \cdot a_{22}=2 \cdot a_{23}=8$
So, the matrix $=\left[\begin{array}{lll}\frac{1}{2} & \frac{9}{2} & \frac{25}{2} \\ 0 & 2 & 8\end{array}\right]$
Conclusion: Therefore, Matrix is $\left[\begin{array}{lll}\frac{1}{2} & \frac{9}{2} & \frac{25}{2} \\ 0 & 2 & 8\end{array}\right]$
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