The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

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.
- $$\left[ \begin{array} { r r r r r } 1 & 4 & - 2 & - 3 & 1 \\0 & 0 & 1 & 4 & - 4 \\- 1 & - 4 & 0 & - 5 & 7\end{array} \right]$$

A) $x _ { 1 } = - 4 x _ { 2 } + 2 x _ { 3 } + 3 x _ { 4 } + 1$
$x _ { 2 }$ is free
$x _ { 3 } = - 4 - 4 x _ { 4 }$
$x _ { 4 }$ is free

B) $\times _ { 1 } = - 7 - 4 \times _ { 2 } - 5 x _ { 4 }$
$x _ { 2 }$ is free
$x _ { 3 } = - 4 - 4 x _ { 4 }$
$x _ { 4 }$ is free

C) $x _ { 1 } = - 7 - 4 x _ { 2 } - 5 x _ { 4 }$
$x _ { 2 }$ is free
$x _ { 3 } = - 4 - 4 x _ { 4 }$
$x _ { 4 } = 0$

D) $x _ { 1 } = - 7 - 4 x _ { 2 } - 5 \times 3$
$x _ { 2 } = - 4 - 4 x _ { 3 }$
$x _ { 3 }$ is free