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# Construct $a_{2\times 2}$ matrix where $a_{ij} =\frac{(i + 2j)^2}{2}$

Toolbox:
• In general $a_{2\times 2}$ matrix is given by $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21} &a_{22}\end{bmatrix}$
Step1:
Elements are given by
$a_{ij}=\frac{(i+2j)^2}{2}$
Replace i=1,j=1.
$a_{11}=\frac{(1+2(1))^2}{2}$
$\;\;\;=\frac{(1+2)^2}{2}=\frac{3^2}{2}=9/2.$
$a_{12}=\frac{(1+2(2))^2}{2}$
Replace i=1,j=2.
$\;\;\;=\frac{(1+4)^2}{2}=\frac{5^2}{2}=25/2.$
Step2
$a_{21}=\frac{(2+2(1))^2}{2}$
Replace i=2,j=1.
$\;\;\;=\frac{(2+2)^2}{2}=\frac{4^2}{2}=16/2=8$
$a_{22}=\frac{(2+2(2))^2}{2}$
Replace i=2,j=2.
$\;\;\;=\frac{(2+4)^2}{2}=\frac{6^2}{2}=36/2=18$
Step3:
Hence the required matrix is given by$A=\begin{bmatrix}9/2 & 25/2\\8 &18\end{bmatrix}$