Question

Construct a $2\times 3$ matrix $A=\left[a_{ij}\right]$ whose elements are given by $a_{ij}=\{\begin{array}{c}i-ji\ge j\\ i+ji<j\end{array}$

Answer 1

We have $\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\end{array}\right]$

Since $a_{ij}=\{\begin{array}{c}i-ji\ge j\\ i+ji<j\end{array}$

$a_{11}=1-1=0$

$a_{12}=1+2=3$

$a_{13}=1+3=4$

$a_{21}=2-1=1$

$a_{22}=2-2=0$

$a_{23}=2+3=5$

Hence the required matrix is

$A=\left[\begin{array}{ccc}0& 3& 4\\ 1& 0& 5\end{array}\right]$