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

Question

Construct a 2 × 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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