Question:
Construct a $2 \times 2$ matrix whose elements are $\mathrm{a}_{\mathrm{ij}}=\frac{(\mathrm{i}+2 \mathrm{j})^{2}}{2}$
Solution:
It is a $(2 \times 2)$ matrix. So, it has 2 rows and 2 columns.
Given $a_{i j}=\frac{((t+2))^{2}}{2}$
So, $a_{11}=\frac{9}{2}, a_{12}=\frac{25}{2}$,
$a_{21}=8, a_{22}=18$
So, the matrix $=\left[\begin{array}{cc}\frac{9}{2} & \frac{25}{2} \\ 8 & 18\end{array}\right]$
Conclusion: Therefore, Matrix is $=\left[\begin{array}{cc}\frac{9}{2} & \frac{25}{2} \\ 8 & 18\end{array}\right]$