Question

Construct a $2\times 2$ matrix $A=\left[a_{ij}\right]$, whose element $a_{ij}$ is $\frac{(i+j{)}^2}{2}$.

Answer 1

$\Rightarrow$ $a_{ij}=\frac{(i+j{)}^2}{2}$

$a_{ij}$	$i=,j=$	$a_{ij}=\frac{(i+j{)}^2}{2}$
$a_{11}$	$i=1,j=1$	$a_{11}=\frac{(1+1{)}^2}{2}=\frac{(2{)}^2}{2}=\frac{4}{2}=2$
$a_{12}$	$i=1,j=2$	$a_{12}=\frac{(1+2{)}^2}{2}=\frac{(3{)}^2}{2}=\frac{9}{2}$
$a_{21}$	$i=2,j=1$	$a_{21}=\frac{(2+1{)}^2}{2}=\frac{(3{)}^2}{2}=\frac{9}{2}$
$a_{22}$	$i=2,j=2$	$a_{22}=\frac{(2+2{)}^2}{2}=\frac{(4{)}^2}{2}=\frac{16}{2}=8$

$\Rightarrow$ Required matrix $A=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}2& \frac{9}{2}\\ \frac{9}{2}& 8\end{array}\right]$