If $a_{ij}=\hat i+3\hat j$, then the matrix of order 2 with elements as $a_{ij}$ is
Answer & explanation
Correct answer: option 3
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 $\begin{bmatrix}4 & 7 \\ 5 & 8\end{bmatrix}$.