Question
Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by
$\frac{(i+2 j)^2}{2}$.
$\frac{(i+2 j)^2}{2}$.
✓
Answer
$ \text { We have } a _{ ij }=\frac{(i+2 j)^2}{2}$
$a _{11}=\frac{(1+2 \times 1)^2}{2}=\frac{9}{2}$
$a _{12}=\frac{(1+2 \times 1)^2}{2}=\frac{25}{2}$
$a_{21}=\frac{(2+2 \times 1)^2}{2}=\frac{16}{2}=8$
$a_{22}=\frac{(2+2 \times 2)^2}{2}=18 $
The required matrix
$
\begin{aligned}
A & =\left[\begin{array}{ll}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{array}\right] \\
A & =\left[\begin{array}{cc}
\frac{9}{2} & \frac{25}{2} \\
8 & 18
\end{array}\right] .
\end{aligned}
$
$a _{11}=\frac{(1+2 \times 1)^2}{2}=\frac{9}{2}$
$a _{12}=\frac{(1+2 \times 1)^2}{2}=\frac{25}{2}$
$a_{21}=\frac{(2+2 \times 1)^2}{2}=\frac{16}{2}=8$
$a_{22}=\frac{(2+2 \times 2)^2}{2}=18 $
The required matrix
$
\begin{aligned}
A & =\left[\begin{array}{ll}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{array}\right] \\
A & =\left[\begin{array}{cc}
\frac{9}{2} & \frac{25}{2} \\
8 & 18
\end{array}\right] .
\end{aligned}
$
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