Evaluate the determinant of the matrix.

• A. $\frac{107}{3}$
• B. $\frac{227}{6}$
• C. 33
• D. 12

Answer: (C)

Verified step by step guidance

1. Identify the elements of the 2x2 matrix: a = 4, b = \frac{9}{2}, c = \frac{2}{3}, d = 9.
2. Recall the formula for the determinant of a 2x2 matrix: det(A) = ad - bc.
3. Substitute the identified elements into the determinant formula: det(A) = (4)(9) - (\frac{9}{2})(\frac{2}{3}).
4. Calculate the product of the diagonal elements: 4 * 9.
5. Calculate the product of the off-diagonal elements: \frac{9}{2} * \frac{2}{3}.