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

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.
- $$\left[ \begin{array} { r r r r } 1 & 0 & 6 & 3 \\0 & 1 & - 2 & - 3 \\0 & 0 & 0 & 0\end{array} \right]$$

A) $x _ { 1 } = 3 - 6 x _ { 3 }$
$x _ { 2 } = - 3 + 2 x _ { 3 }$
$x _ { 3 } = 0$

B) $x _ { 1 } = 3 - 6 x _ { 3 }$
$x _ { 2 }$ is free
$x _ { 3 } = \frac { 3 } { 2 } + \frac { 1 } { 2 } x _ { 2 }$

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

D) No solution