Construct a2 × 2 matrix where

Solution:

We have,

A = [aij]2×2

(i) Such that, aij = (i – 2j)2/ 2; where 1 ≤ i ≤ 2; 1 ≤ j ≤ 2

So, the terms of the matrix are

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

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

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

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

Therefore, $A=\left[\begin{array}{ll}\frac{1}{2} & \frac{9}{2} \\ 0 & 2\end{array}\right]$

(ii) Here, aij = |-2i + 3j|

So, the terms of the matrix are

$a_{11}=|-2 \times 1+3 \times 1|=1$

$a_{12}=|-2 \times 1+3 \times 2|=4$

$a_{21}=|-2 \times 2+3 \times 1|=1$

$a_{22}=|-2 \times 2+3 \times 2|=2$

Therefore, $A=\left[\begin{array}{ll}1 & 4 \\ 1 & 2\end{array}\right]$