Question
Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij}= 2i - j$
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Answer
We have $a_{i j}=2 i-j$
Now $a_{11}=2 \times 1-1=1$
$ a_{12}=2 \times 1-2=0$
$a_{21}=2 \times 2-1=3$
$a_{22}=2 \times 2-2=2 $
So the required matrix
$ \begin{array}{l} A =\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \end{array}$
$A =\left[\begin{array}{ll} 1 & 0 \\ 3 & 2 \end{array}\right] .$
Now $a_{11}=2 \times 1-1=1$
$ a_{12}=2 \times 1-2=0$
$a_{21}=2 \times 2-1=3$
$a_{22}=2 \times 2-2=2 $
So the required matrix
$ \begin{array}{l} A =\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right] \end{array}$
$A =\left[\begin{array}{ll} 1 & 0 \\ 3 & 2 \end{array}\right] .$
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