The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

Multiple Choice

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
- $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & - 6 \\0 & 1 & 4 & 7 \\0 & 0 & 0 & 2\end{array} \right]$$

A) $x _ { 1 } = - 20 + 11 x _ { 3 }$
$$\begin{array} { l } x _ { 2 } = 7 - 4 x _ { 3 } \\x _ { 3 } = 2\end{array}$$
B) No solution

C) $x _ { 1 } = - 6 - 2 x _ { 2 } + 3 x _ { 3 }$
$x _ { 2 }$ is free
$x _ { 3 }$ is free

D) $\mathrm { x } _ { 1 } = - 20 + 11 \mathrm { x } _ { 3 }$
$x _ { 2 } = 7 - 4 x _ { 3 }$
$x _ { 3 }$ is free