Question

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

• A. $\left[\begin{array}{cc}1& 3\\ 0& 2\\ -1& 1\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 3& 5\\ 0& 2& 4\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 0\\ 3& 2\\ 5& 4\end{array}\right]$
• D. $\left[\begin{array}{ccc}1& 0& -1\\ 3& 2& 1\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}1& 0\\ 3& 2\\ 5& 4\end{array}\right]$

In general 3 $\times$ 2 matrix is given by $\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right]$
Now $a_{ij}=2i-j$
$\Rightarrow a_{11}=2\left(1\right)-1=1$
$a_{12}=2\left(1\right)-2=0$
$a_{21}=2\left(2\right)-1=3$
$a_{22}=2\left(2\right)-2=2$
$a_{31}=2\left(3\right)-1=5$
$a_{32}=2\left(3\right)-2=4$
Hence required matrix is, $\left[\begin{array}{cc}1& 0\\ 3& 2\\ 5& 4\end{array}\right]$