Answer
$0$
Work Step by Step
The determinant for a 3 by 3 matrix can be computed as: $det= \begin{vmatrix} A & B & C \\
a & b & c \\
g &h & i \\ \end{vmatrix}=A(bi-eh)-B(ai-eg)+C(ah-bg)$
Therefore, the determinant of the given matrix is:
$det=\begin{vmatrix} -3 & 2 & 7 \\
6 & -4 & -14 \\7 &1 &4 \\ \end{vmatrix} \\=-3[(-4)(4)-(-14)(1)]-2[(6)(4)-(-14)(7)]+7[(6)(1)-(-4)(7)]\\=-3(-16+14)-2(24+98)+7(6+28)\\=0$
