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:
$\text{a}_\text{ij}=\frac{|2\text{i}-3\text{j}|}{2}$

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Answer

Here,
$\text{a}_{11}=\frac{|2(1)-3(1)|}{2}=\frac{1}{2},$ $\text{a}_{12}=\frac{|2(1)-3(2)|}{2}=2$
$\text{a}_{21}=\frac{|2(2)-3(1)|}{2}=\frac{1}{2},$ $\text{a}_{22}=\frac{|2(2)-3(2)|}{2}=1$
Using equation $(i)$
$\text{A}=\begin{bmatrix}\frac{1}{2}&2\\\frac{1}{2}&1\end{bmatrix}$

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