Write the System of Linear Equations as a Matrix Equation $A X = B$

Write the system of linear equations as a matrix equation $A X = B$ , and use Gauss-Jordan elimination on the augmented matrix $[ A \vdots B ]$ to solve for the matrix $X$ .
$$\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } - 9 x _ { 3 } & = 43 \\x _ { 1 } + 4 x _ { 2 } + 7 x _ { 3 } & = - 51 \\7 x _ { 1 } - 7 x _ { 2 } + 3 x _ { 3 } & = - 57\end{aligned} \right.$$

A)
$X = \left[ \begin{array} { c } - 16 \\ 10 \\ - 40 \end{array} \right]$
B)
$X = \left[ \begin{array} { c } 10 \\ 8 \\ - 2 \end{array} \right]$
C)
$X = \left[ \begin{array} { l } - 8 \\ - 2 \\ - 5 \end{array} \right]$
D)
$X = \left[ \begin{array} { c } - 10 \\ 16 \\ 40 \end{array} \right]$
E)
$X = \left[ \begin{array} { c } 8 \\ 5 \\ - 2 \end{array} \right]$