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# Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by:$(ii) a_{ij}=\frac{i}{j}\qquad$

Note: This is a 3 part question, split as 3 separate questions here

Toolbox:
• In general $a_{2\times 2}$ matrix is given by$\begin{bmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{bmatrix}$
• Elements are given by $a_{ij}=\frac{i}{j}$, where (i, j) can be either (1,1), (1,2), (2,2) or (2,1)
Given, $a_{ij}=\frac{i}{j} \Rightarrow$
$a_{11}=\frac{1}{1}=1.$
$a_{12}=\frac{1}{2}.$
$a_{21}=\frac{2}{1}=2.$
$a_{22}=\frac{2}{2}=1.$
Hence the required matrix is given by $A=\begin{bmatrix}1 & \frac{1}{2}\\2 & 1\end{bmatrix}$