Construct a 3 × 4 matrix whose elements are given by

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

Given $a_{i j}=\frac{|-3 i+j|}{2}$

So, $a_{11}=1, a_{12}=\frac{1}{2}, a_{13}=0, a_{13}=\frac{1}{2}$,

$a_{21}=\frac{5}{2}, a_{22}=2, a_{23}=\frac{3}{2}, a_{13}=1$

$a_{31}=4, a_{32}=\frac{7}{2}, a_{33}=3, a_{13}=\frac{5}{2}$

So, the matrix $=\left[\begin{array}{cccc}1 & \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{5}{2} & 2 & \frac{3}{2} & 1 \\ 4 & \frac{7}{2} & 3 & \frac{5}{2}\end{array}\right]$

Conclusion: Therefore, Matrix is $\left[\begin{array}{cccc}1 & \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{5}{2} & 2 & \frac{3}{2} & 1 \\ 4 & \frac{7}{2} & 3 & \frac{5}{2}\end{array}\right]$