Question

If $A={\left(a_{ij}\right)}_{2\times 2}$, where $a_{ij}=i+j$, then $A$ is equal to:

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

Answer 1

Answer: (C)

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

$a_{ij}=i+j$

$\therefore a_{11}=1+1=2$

$a_{12}=1+2=3$

$a_{21}=2+1=3$

$a_{22}=2+2=4$

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