Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
$\left[ \begin{array} { c c c }
1 & 0 & 4 \
1 & - 4 & 2 \
- 1 & 2 & 3
\end{array} \right]$
A) -5
B) 11
C) 8
D) -24
E) -4

Question

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. 
$\left[ \begin{array} { c c c } 
1 & 0 & 4 \
1 & - 4 & 2 \
- 1 & 2 & 3
\end{array} \right]$
A) -5
B) 11
C) 8
D) -24
E) -4

Quizplus · Accepted Answer

Expanding along the first column gives $$-1\begin{bmatrix} 1&2 \-4&2 \end{bmatrix} -4\begin{bmatrix}1&4 \ -1&3\end{bmatrix}+0\begin{bmatrix} 1&1\-4&-1\end{bmatrix} = -1(-8)-4(13)+0 = \boxed{-24}.$$

Evaluate the Determinant of the Matrix [1041−42−123]\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]​11−1​0−42​423​​

Evaluate the Determinant of the Matrix $\left[ \begin{array} { c c c } 1 & 0 & 4 \\1 & - 4 & 2 \\- 1 & 2 & 3\end{array} \right]$