If $a_{ij}=\hat i+3\hat j$, then the matrix of order 2 with elements as $a_{ij}$ is

$\begin{bmatrix}4&7\\5&8\end{bmatrix}$

The correct answer is Option (3) → $\begin{bmatrix}4&7\\5&8\end{bmatrix}$ **

Given: $a_{ij} = i + 3j$

For a $2 \times 2$ matrix, $i,j = 1,2$

$a_{11} = 1 + 3\cdot 1 = 4$

$a_{12} = 1 + 3\cdot 2 = 7$

$a_{21} = 2 + 3\cdot 1 = 5$

$a_{22} = 2 + 3\cdot 2 = 8$

Matrix = $\begin{bmatrix}4 & 7 \\ 5 & 8\end{bmatrix}$

The required $2 \times 2$ matrix is $\begin{bmatrix}4 & 7 \\ 5 & 8\end{bmatrix}$.