Question

If $A=[a_{ij}{]}_{2\times 2}$ and $a_{ij}=i+j$, then A =

• A. $[\begin{array}{cc}1& 2\\ 3& 4\end{array}]$
• B. $[\begin{array}{cc}2& 3\\ 3& 4\end{array}]$
• C. $[\begin{array}{cc}2& 3\\ 4& 5\end{array}]$
• D. $[\begin{array}{cc}4& 5\\ 6& 7\end{array}]$

Answer 1

The correct option is B $[\begin{array}{cc}2& 3\\ 3& 4\end{array}]$

$A={\left[a_{ij}\right]}_{2\times 2}$

$a_{ij}=1+j$

$\Rightarrow a_{11}=1+1=2,a_{12}=1+2=3$

$\Rightarrow a_{21}=2+1=3,a_{22}=2+2=4$

$\Rightarrow A=\left[\begin{array}{cc}2& 3\\ 3& 4\end{array}\right]$

Hence, the answer is $\left[\begin{array}{cc}2& 3\\ 3& 4\end{array}\right].$