Find the System of Equations That the Following Augmented Matrix $\left[ \begin{array} { c c c : c } 1 & - 6 & 2 & - 5 \\2 & 0 & 8 & 8 \\6 & - 8 & 6 & 1\end{array} \right]$

Multiple Choice

Find the system of equations that the following augmented matrix represents. $\left[ \begin{array} { c c c : c } 1 & - 6 & 2 & - 5 \\2 & 0 & 8 & 8 \\6 & - 8 & 6 & 1\end{array} \right]$

A) $\left\{ \begin{array} { l } x - 6 y + 2 z - 5 w = 0 \\2 x + y + 8 z + 8 w = 0 \\6 x - 8 y + 6 z - w = 0\end{array} \right.$
B) $\left\{ \begin{array} { l } x - 6 y + 2 z = - 5 \\2 x + 8 z = 8 \\6 x - 8 y + 6 z = 1\end{array} \right.$
C) $\left\{ \begin{array} { l } x + 6 y + 2 z = - 5 \\2 x + y + 8 z = 8 \\6 x - 8 y + 6 z = - 1\end{array} \right.$
D) $\left\{ \begin{array} { l } x - 6 y + 2 z = - 5 \\2 x + y + 8 z = 8 \\6 x - 8 y + 6 z = - 1\end{array} \right.$