Find the determinant of the matrix below.Expand by cofactors on the row or column that appears to make the computations easiest.
A) -20
B) -216
C) 120
D) 456
E) 180

Question

Find the determinant of the matrix below.Expand by cofactors on the row or column that appears to make the computations easiest. 
A) -20 
B) -216 
C) 120 
D) 456 
E) 180

Quizplus · Accepted Answer

Expanding along the first row, we have 
$$\det\begin{pmatrix} 3 & -2 & 4 \ 0 & 1 & -1 \ -4 & 3 & 0 \end{pmatrix} = 3\det\begin{pmatrix}1 & -1 \ 3 & 0\end{pmatrix} - (-2)\det\begin{pmatrix} 0 & -1 \ -4 & 0 \end{pmatrix} + 4\det\begin{pmatrix} 0 & 1 \ -4 & 3 \end{pmatrix}.$$

Evaluating the determinants, we find that we get

$$3(3) - (-2)(-4) + 4(-4) = 9 + 8 - 16 = \boxed{C) \ 120}.$$

Find the Determinant of the Matrix Below