Question

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

Answer 1

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

$\Rightarrow a_{11}=\frac{(1-2{)}^2}{2}=\frac{1}{2}$ $,$ $a_{12}=\frac{(1-4{)}^2}{2}=\frac{9}{2}$

$\Rightarrow a_{21}=\frac{(2-2{)}^2}{2}=0$ $,$ $a_{22}=\frac{(2-4{)}^2}{2}=2$

$\Rightarrow a_{31}=\frac{(3-2{)}^2}{2}=\frac{1}{2}$ $,$ $a_{32}=\frac{(3-4{)}^2}{2}=\frac{1}{2}$

$\therefore A=\left[\begin{array}{cc}\frac{1}{2}& \frac{9}{2}\\ 0& 2\\ \frac{1}{2}& \frac{1}{2}\end{array}\right]$

Hence, solved.