To determine which expression represents the determinant of matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 9 \end{bmatrix}$, we can use the formula for the determinant of a 2x2 matrix:

$\text{det}(A) = ad - bc$

where $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$.

In this case:

• $a = 2$
• $b = 3$
• $c = 1$
• $d = 9$

Plugging in the values:

$\text{det}(A) = (2)(9) - (3)(1)$

Calculating this:

$\text{det}(A) = 18 - 3 = 15$

Thus, the correct answer is:

• $\text{det}(A) = (2)(9) - (1)(3)$

This corresponds to the first option in the list.

Would you like more details on determinants or further assistance with similar questions?

Related Questions:

1. How is the determinant of a 3x3 matrix calculated?
2. What is the geometric interpretation of a determinant?
3. How does a determinant help in solving linear equations?
4. What happens to the determinant if we swap two rows in a matrix?
5. How does scaling a row of a matrix affect the determinant?

Tip: Remember that the determinant of a 2x2 matrix is simply the product of the main diagonal elements minus the product of the off-diagonal elements.