Question

Construct a $2\times 2$ matrix $A=\left[a_{ij}\right]$, whose elements are given by $a_{ij}=\frac{i}{j}$.

Answer 1

$A=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]a_{11}=\frac{1}{1}=1a_{21}=\frac{2}{1}=2$

$a_{12}=\frac{1}{2}{a}_{22}=\frac{2}{2}=1$
$\therefore A=\left[\begin{array}{cc}1& \frac{1}{2}\\ 2& 1\end{array}\right]$.