Question

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

Answer 1

We have $a3\times 2$ matrix $A.$

$A=[aij{]}_{3\times 2}$ has $3$ rows & $2$

Columns

$A={\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right]}_{3\times 2.}$ , here $aij=2i-j$

So, $a_{11}=2\left(1\right)-\left(1\right)=1$

$a_{12}=2\left(1\right)-\left(2\right)=0$

$a_{21}=2\left(2\right)-\left(1\right)=3$

$a_{22}=2\left(2\right)-\left(2\right)=2$

$a_{31}=2\left(3\right)-\left(1\right)=5$

$a_{32}=2\left(3\right)-\left(2\right)=4$

So, $A={\left[\begin{array}{cc}1& 0\\ 3& 2\\ 5& 4\end{array}\right]}_{3\times 2.}$