Construct a 2 2 matrix A = [a_ ij ] whose elements a_ ij are give… - Vidyadip

Question

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

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Answer

Here,
$\text{a}_{11}=\frac{(1-1)^2}{2}=0,$
$\text{a}_{12}=\frac{(1+2)^2}{2}=\frac{1}{2},$
$\text{a}_{21}=\frac{(2-1)^2}{2}=\frac{1}{2},$
$\text{a}_{22}=\frac{(2-2)^2}{2}=0,$
Using equation $(i)$
$\text{A}=\begin{bmatrix}0&\frac{1}{2}\\\frac{1}{2}&0\end{bmatrix}$

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