Construct a 3 3 matrix whose elements are given by a _ ij =| i -2… - Vidyadip

Question

Construct a $3 \times 3$ matrix whose elements are given by $a _{ ij }=| i -2 j |$

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Answer

$
a_{i j}=|i-2 j|
$

The general $3 \times 3$ matrices is
$
\begin{aligned}
& A=\left[\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33}
\end{array}\right] \\
& a_{11}=|1-2(1)|=|1-2|=|-1|=1 \\
& a_{12}=|1-2(2)|=|1-4|=|-3|=3 \\
& a_{13}=|1-2(3)|=|1-6|=|-5|=5 \\
& a_{21}=|2-2(1)|=|2-2|=0=0 \\
& a_{22}=|2-2(2)|=|2-4|=|-2|=2 \\
& a_{23}=|2-2(3)|=|2-6|=|-4|=4 \\
& a_{31}=|3-2(1)|=|3-2|=|1|=1 \\
& a_{32}=|3-2(2)|=|3-4|=|-1|=1 \\
& a_{33}=|3-2(3)|=|3-6|=|-3|=3
\end{aligned}
$
The required matrix $A=\left[\begin{array}{lll}1 & 3 & 5 \\ 0 & 2 & 4 \\ 1 & 1 & 3\end{array}\right]$

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