Find the determinant of the following matrix: \[ A = \begin{bmatrix} 4 & 3 & 2 \\ 3 & 2 & 1 \\ 2 & 1 & 4 \end{bmatrix} \]

Step 1 ：The determinant of a 3x3 matrix can be calculated using the formula: \[ det(A) = a(ei−fh)−b(di−fg)+c(dh−eg) \] where \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \]

Step 2 ：Substituting the values from matrix A into the formula, we get: \[ det(A) = 4(2*4−1*1)−3(3*4−2*1)+2(3*1−2*2) \]

Step 3 ：Calculating the above expression, we get: \[ det(A) = 4(8−1)−3(12−2)+2(3−4) \]

Step 4 ：Further simplifying, we get: \[ det(A) = 4*7−3*10+2*(-1) \]

Step 5 ：Finally, we have: \[ det(A) = 28−30−2 \]