Question

Construct a $2\times 3$ matrix $A=\left[a_{ij}\right]$ whose elements are given by $a_{ij}=|2i-3j|$

Answer 1

Let $A=\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\end{array}\right)$
$a_{ij}=|2i-3j|$
$a_{11}=|2\left(1\right)-\left(3\right)\left(1\right)|=|2-3|=|-1|=1$
$a_{12}=|2\left(1\right)-\left(3\right)\left(2\right)|=|2-6|=|-4|=4$
$a_{13}=|2\left(1\right)-3\left(3\right)|=|2-9|=|-7|=7$
$a_{21}=|2\left(2\right)-3\left(1\right)|=|4-3|=1$
$a_{22}=|2\left(2\right)-3\left(2\right)|=|4-6|=|-2|=2$
$a_{23}=|2\left(2\right)-3\left(3\right)|=|4-9|=|-5|=5$
Therefore, $A=\left(\begin{array}{ccc}1& 4& 7\\ 1& 2& 5\end{array}\right)$