Question

Construct a $2\times 2$ matrix, where

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

Answer 1

We know that the notation, namely A = $[a_{ij}{]}_{m\times n}$, indicates that A is a matrix of order m $\times$ n. Also, $1\le i\le m,1\le j\le n;i,jϵN.$

(i) Here, A = $[a_{ij}{]}_{2\times 2}$

$\Rightarrow A=\frac{(i-2j{)}^2}{2},1\le i\le 2:1\le j\le 2$,

$\therefore a_{11}=\frac{(1-2{)}^2}{2}=\frac{1}{2}$

$a_{12}=\frac{(1-2\times 2{)}^2}{2}=\frac{9}{2}$

$a_{21}=\frac{(2-2\times 1{)}^2}{2}=0$

$a_{22}=\frac{(2-2\times 2{)}^2}{2}=2$

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