Answer
$-200$
Work Step by Step
We are given the determinant:
$D=\begin{vmatrix}4&2&8&-7\\-2&0&4&1\\5&0&0&5\\4&0&0&-1\end{vmatrix}$
In order to compute the determinant we expand it along the second column because it has 3 zeros:
$D=-2D_{12}+0D_{22}-0D_{32}+0D_{43}=-2D_{12}$
$=-2\begin{vmatrix}-2&4&1\\5&0&5\\4&0&-1\end{vmatrix}$
We expand the $3\times 3$ determinant along the second column:
$D=-2\cdot 4\begin{vmatrix}5&5\\4&-1\end{vmatrix}=-8(-5-20)=-200$
