Answer
23 cubic units
Work Step by Step
To find the volume of the parallelepiped with one vertex at
the origin;
given the vertices as;
$\textbf{v1}=\begin{bmatrix}1\\0\\-3\end{bmatrix}$
$\textbf{v2}=\begin{bmatrix}1\\2\\4\end{bmatrix}$
$\textbf{v3}=\begin{bmatrix}5\\1\\0\end{bmatrix}$
the adjacent vectors form a Matrix $\textbf{A}$
$\textbf{A}=\begin{bmatrix}1&1&5\\0&2&1\\-3&4&0\end{bmatrix}$
volume of the parallelepiped is found as;
$volume= |det A|=|1\begin{vmatrix}2&1\\4&0\end{vmatrix}-0\begin{vmatrix}1&5\\4&0\end{vmatrix}-3\begin{vmatrix}1&5\\2&1\end{vmatrix}|$
$volume=|1(0-4)-0-3(1-10)|=|23|=23$ cubic units
