Question

if $A=\left[a_{ij}\right]_{2\times2}$, where $a_{ij} = \frac{\left(i+2j\right)^{2} }{2}$, then A is equal to

• A. $\begin{bmatrix}9&25\\ 8&18\end{bmatrix}$
• B. $\begin{bmatrix}9/2&25/2\\8&18\end{bmatrix}$
• C. $\begin{bmatrix}9&25\\ 4&9\end{bmatrix}$
• D. $\begin{bmatrix}\frac{9}{2}&\frac{15}{2}\\ 4&9\end{bmatrix}$

Answer 1

Answer: (B)

Here,
$ a_{11} =\frac{1+2+1^{2} }{ 2}= \frac{9 }{2}$
$a_{12} = \frac{\left(1+2\times2\right)^{2} }{2 }= \frac{25 }{2 }$
$a_{21}=\frac{\left(1+2\times1\right)^{2}}{2} = 8 \,\,and\,\,$
$ a_{22} =\frac{\left(1+2\times2\right)^{2}}{2} = 18$
So,the required matrix $A = \begin{bmatrix}\frac{9}{2}&\frac{25}{2}\\ 8&18\end{bmatrix}$