Question

if $A={\left[a_{ij}\right]}_{2\times 2}$, where $a_{ij}=\frac{{\left(i+2j\right)}^2}{2}$, then A is equal to

• A. $\left[\begin{array}{cc}9& 25\\ 8& 18\end{array}\right]$
• B. $\left[\begin{array}{cc}9/2& 25/2\\ 8& 18\end{array}\right]$
• C. $\left[\begin{array}{cc}9& 25\\ 4& 9\end{array}\right]$
• D. $\left[\begin{array}{cc}\frac{9}{2}& \frac{15}{2}\\ 4& 9\end{array}\right]$

Answer 1

Answer: (B)

Here,
$a_{11}=\frac{1+2+1^2}{2}=\frac{9}{2}$
$a_{12}=\frac{{\left(1+2\times 2\right)}^2}{2}=\frac{25}{2}$
$a_{21}=\frac{{\left(1+2\times 1\right)}^2}{2}=8and$
$a_{22}=\frac{{\left(1+2\times 2\right)}^2}{2}=18$
So,the required matrix $A=\left[\begin{array}{cc}\frac{9}{2}& \frac{25}{2}\\ 8& 18\end{array}\right]$