Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by: $a_{ij} = \frac{(i + 2j)^2}{2}$

(N/A) Since it is a $2 \times 2$ matrix,it has $2$ rows and $2$ columns. Let the matrix be $A$.
Where $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$.
Now,it is given that $a_{ij} = \frac{(i + 2j)^2}{2}$.

Element	Calculation
$a_{11}$	$a_{11} = \frac{(1 + 2(1))^2}{2} = \frac{(1 + 2)^2}{2} = \frac{3^2}{2} = \frac{9}{2}$
$a_{12}$	$a_{12} = \frac{(1 + 2(2))^2}{2} = \frac{(1 + 4)^2}{2} = \frac{5^2}{2} = \frac{25}{2}$
$a_{21}$	$a_{21} = \frac{(2 + 2(1))^2}{2} = \frac{(2 + 2)^2}{2} = \frac{4^2}{2} = \frac{16}{2} = 8$
$a_{22}$	$a_{22} = \frac{(2 + 2(2))^2}{2} = \frac{(2 + 4)^2}{2} = \frac{6^2}{2} = \frac{36}{2} = 18$

Hence,the required matrix $A$ is:
$A = \begin{bmatrix} \frac{9}{2} & \frac{25}{2} \\ 8 & 18 \end{bmatrix}$