Answer
See below
Work Step by Step
Given
$\begin{bmatrix}
7 &1 & 2 & 3\\2 & -2 & 4 &6\\3&-1&5&4\\18&9&27&54
\end{bmatrix}\approx \begin{bmatrix}
7 &8 & 2 & 3\\2 & 0 & 4 &6\\3&2&5&4\\18&27&27&54
\end{bmatrix}\approx \begin{bmatrix}
7 &8 & -12 & 3\\2 & 0 & 0 &6\\3&2&-1&4\\18&27&-9&54
\end{bmatrix}\approx\begin{bmatrix}
7 &8 & -12 & -18\\2 & 0 & 0 &0\\3&2&-1&-5\\18&27&-9&0
\end{bmatrix}$
the determinant
$D=-2\begin{vmatrix}
8 & -12 & -18\\2&-1&-5\\27&-9&0
\end{vmatrix}$
Hence here
$D=-2.2.9[3(30-9)-20+18]$
$D=-2196$
