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

Here, a_ 11 =|-3(1)+1| 2 =|-3+1| 2 =|-2| 2 =1, a_ 12 =|-3(1)+2| 2 =|-3+2| 2 =|-1| 2 =1 2 a_ 21 =|-3(2)+1| 2 =|-6+1| 2 =|-5| 2 =5 2 , a_ 22 =|-3(2)+2| 2 =|-6+2| 2 =|-4| 2 =2 So, the required matrix is 1&1 2 5 2 &2 .

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

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Answer

Here,
$\text{a}_{11}=\frac{|-3(1)+1|}{2}=\frac{|-3+1|}{2}=\frac{|-2|}{2}=1,$ $\text{a}_{12}=\frac{|-3(1)+2|}{2}=\frac{|-3+2|}{2}=\frac{|-1|}{2}=\frac{1}{2}$
$\text{a}_{21}=\frac{|-3(2)+1|}{2}=\frac{|-6+1|}{2}=\frac{|-5|}{2}=\frac{5}{2},$ $\text{a}_{22}=\frac{|-3(2)+2|}{2}=\frac{|-6+2|}{2}=\frac{|-4|}{2}=2$
So, the required matrix is $\begin{bmatrix}1&\frac{1}{2}\\\frac{5}{2}&2\end{bmatrix}.$

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