Answer
$56$
Work Step by Step
Given: $$\begin{array}{c}{A=\left[\begin{array}{ccc}{2} & {-1} & {4} \\ {3} & {2} & {1} \\ {-2} & {1} & {4}\end{array}\right] }\end{array} $$
Perform row operations $R_2 \rightarrow R_2-\dfrac{3R_1}{2}$ and $R_3 \rightarrow R_3+R_1$ to obtain:
$$A=\begin{vmatrix}{2} & {-1} & {4} \\ {0} & {7/2} & {-5} \\ {0} & {0} & {8}\end{vmatrix}$$
Determinant of triangular matrix is the product of its diagonal elements, so: $det (A)=(2)(\dfrac{7}{2})(8)=56$
