Construct a 2 × 2 matrix A = [aij] whose elements aij are given b…

Question

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by:
$\text{a}_\text{ij}=\frac{(2\text{i}-\text{j})^2}{2}$

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Answer

Here,
$\text{a}_{11}=\frac{[2(1)+1]^2}{2}=\frac{(2+1)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2},$ $\text{a}_{12}=\frac{[2(1)+2]^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}=8$
$\text{a}_{21}=\frac{[2(2)+1]^2}{2}=\frac{(4+1)^2}{2}=\frac{(5)^2}{2}=\frac{25}{2},$ $\text{a}_{22}=\frac{[2(2)+2]^2}{2}=\frac{(4+2)^2}{2}=\frac{(6)^2}{2}=\frac{36}{2}=18$
So, the required matrix is $\begin{bmatrix}\frac{9}{2}&8\\\frac{25}{2}&18\end{bmatrix}.$

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