Question:
If $A=\left[a_{i j}\right]$ is a $2 \times 2$ matrix such that $a_{i j}=i+2 j$, write $A .$
Solution:
Here,
$a_{i j}=i+2 j, 1 \leq i \leq 2$ and $1 \leq j \leq 2$
$\therefore a_{11}=1+2(1)=3, a_{12}=1+2(2)=1+4=5$
$\Rightarrow a_{21}=2+2(1)=4$ and $a_{22}=2+2(2)=2+4=6$
$\therefore A=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]=\left[\begin{array}{ll}3 & 5 \\ 4 & 6\end{array}\right]$