evaluate the determinant of the matrix.\nthe determinant is \n(simplify your answer.)\n

Explanation:

Step1: Recall 2x2 determinant formula

For matrix $\begin{bmatrix}a&b\c&d\end{bmatrix}$, determinant is $ad - bc$.

Step2: Substitute values

$a=2, b=4, c=4, d=-7$. So $2\times(-7) - 4\times4$.

Step3: Calculate result

$-14 - 16 = -30$.

Answer:

-30