The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r r r } 1 & 5 & 8 & - 1 & 2 & 5 \\0 & 0 & 0 & - 4 & 3 & 4 \\0 & 0 & 0 & 0 & - 2 & 8\end{array} \right]$$

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.
- $$\left[ \begin{array} { r r r r r r } 1 & 5 & 8 & - 1 & 2 & 5 \\0 & 0 & 0 & - 4 & 3 & 4 \\0 & 0 & 0 & 0 & - 2 & 8\end{array} \right]$$

A) $x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + 9$
$x _ { 2 }$ is free
$x _ { 3 } = - 4$
$x _ { 4 } = \frac { 3 } { 4 } x _ { 5 } - 1$
$$x _ { 5 } = - 4$$

B) No solution


C) $x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + x _ { 4 } - 2 x _ { 5 } + 5$
$x _ { 2 }$ is free
$x _ { 3 }$ is free
$$x _ { 4 } = \frac { 3 } { 4 } x _ { 5 } - 1$$
$x _ { 5 } = - 4$

D) $x _ { 1 } = - 5 x _ { 2 } - 8 x _ { 3 } + 9$
$x _ { 2 }$ is free
$x _ { 3 }$ is free
$x _ { 4 } = - 4$
$x _ { 5 } = - 4$