Question

A matrix has 13 elements. The number of possible different orders it can have is

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

If a matrix has $k$ elements, the possible orders correspond to all factor pairs of $k$.

Answer 1

The Correct Option is B

Step 1: Recall the formula for number of elements in a matrix.
If a matrix has order \[ m \times n \] then the total number of elements in the matrix is \[ m \times n \]
Step 2: Use the given information.
The matrix contains \[ 13 \] elements. Thus \[ m \times n = 13 \]
Step 3: Factorize the number 13.
The number \(13\) is a prime number. Thus its only positive factor pairs are \[ 1 \times 13 \] and \[ 13 \times 1 \]
Step 4: Determine possible matrix orders.
Thus the matrix can have the following orders:
\[ 1 \times 13 \] \[ 13 \times 1 \] Hence there are exactly two possible orders.

Step 5: Conclusion.
The number of possible matrix orders is \[ 2 \] Final Answer: $\boxed{2}$