Construct a2 × 2 matrix where
(i) aij = (i – 2j)2/ 2
(ii) aij = |-2i + 3j|
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, $A=\left[\begin{array}{ll}1 & 4 \\ 1 & 2\end{array}\right]$
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