Question

Construct a $3\times 4$ matrix whose elements are given by
$\left(ii\right)a_{ij}=2i-j$.

Answer 1

Here, $A={\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\end{array}\right]}_{3\times 4}$, where $a_{ij}=2i-j$
$\therefore a_{11}=2-1=1,a_{12}=2-2=0a_{13}=2-3=-1a_{14}=2-4=-2a_{21}=4-1=3,a_{22}=4-2=2,a_{23}=4-3=1,a_{24}=4-4=0a_{31}=6-1=5,a_{32}=6-2=4,a_{33}=6-3=3,and{a}_{34}=6-4=2$
Hence, the required matrix is $A={\left[\begin{array}{cccc}1& 0& -1& -2\\ 3& 2& 1& 0\\ 5& 4& 3& 2\end{array}\right]}_{3\times 4}$