Construct a 2 2 matrix A = [a_ ij ] whose elements a_ ij are given by: a_ij= |2i-3j| 2

Here, a_ 11 =|2(1)-3(1)| 2 =1 2 , a_ 12 =|2(1)-3(2)| 2 =2 a_ 21 =|2(2)-3(1)| 2 =1 2 , a_ 22 =|2(2)-3(2)| 2 =1 Using equation (i) A= 1 2 &2 1 2 &1

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

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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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