Construct a 4 × 3 matrix whose elements are given

It is (4 x 3) matrix. So it has 4 rows and 3 columns

Given $a_{i j}=\frac{i}{j}$

So, $a_{11}=1, a_{12}=\frac{1}{2}, a_{13}=\frac{1}{3}$

$a_{21}=2, a_{22}=1, a_{23}=\frac{2}{3}$

$a_{31}=3 \cdot a_{32}=\frac{3}{2}, a_{33}=1$

$a_{41}=4 \cdot a_{42}=2 \cdot a_{43}=\frac{4}{3}$

So, the matrix $=\left[\begin{array}{ccc}1 & \frac{1}{2} & \frac{1}{3} \\ 2 & 1 & \frac{2}{3} \\ 3 & \frac{3}{2} & 1 \\ 4 & 2 & \frac{4}{3}\end{array}\right]$

Conclusion: Therefore, Matrix is $\left[\begin{array}{ccc}1 & \frac{1}{2} & \frac{1}{3} \\ 2 & 1 & \frac{2}{3} \\ 3 & \frac{3}{2} & 1 \\ 4 & 2 & \frac{4}{3}\end{array}\right]$