Question

Construct a $2\times 3$ matrix $A=\left[a_{ij}\right]$ whose elements are given by $a_{ij}=2(i-j)$

• A. $\left[\begin{array}{ccc}0& -2& -4\\ 2& 0& -2\end{array}\right]$
• B. $\left[\begin{array}{ccc}0& -2& 4\\ 2& 0& -2\end{array}\right]$
• C. $\left[\begin{array}{ccc}0& -2& -4\\ 2& 0& 2\end{array}\right]$
• D. $\left[\begin{array}{ccc}0& -2& 4\\ 2& 0& 2\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{ccc}0& -2& -4\\ 2& 0& -2\end{array}\right]$

We have
${\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\end{array}\right]}_{2\times 3}$

where $a_{ij}=2(i-j)$

$\therefore$ elements of new matrix

$a_{11}=2(1-1)=0,a_{12}=2(1-2)=-2,a_{13}=2(1-3)=-4a_{21}=2(2-1)=2,a_{22}=2(2-2)=0,a_{23}=2(2-3)=-2$

$\therefore$ Matrix $=\left[\begin{array}{ccc}0& -2& -4\\ 2& 0& -2\end{array}\right]$