Solve the System of Linear Equations Using the Inverse Matrix

Multiple Choice

Solve the system of linear equations
$\left\{ \begin{array} { l } 4 x _ { 1 } - 8 x _ { 2 } - 4 x _ { 3 } - 8 x _ { 4 } = 0 \\12 x _ { 1 } - 20 x _ { 2 } - 8 x _ { 3 } - 12 x _ { 4 } = - 9 \\8 x _ { 1 } - 20 x _ { 2 } - 8 x _ { 3 } - 20 x _ { 4 } = 6 \\- 4 x _ { 1 } + 16 x _ { 2 } + 16 x _ { 3 } + 44 x _ { 4 } = 0\end{array} \right.$
using the inverse matrix $\frac { 1 } { 4 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\ - 10 & 3 & 0 & - 1 \\ - 29 & 7 & 3 & - 2 \\ 12 & - 3 & - 1 & 1 \end{array} \right]$ .

A)
$\left[\begin{array}{l}x_{1} \\x_{2} \\x_{3} \\x_{4}\end{array}\right]=\left[\begin{array}{r}-\frac{57}{4} \\-\frac{27}{4} \\-\frac{45}{4} \\\frac{21}{4}\end{array}\right]$


B) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 21 } { 4 } \\ - \frac { 15 } { 4 } \\ \frac { 27 } { 4 } \\ - \frac { 27 } { 4 } \end{array} \right]$

C) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 27 } { 4 } \\ - \frac { 57 } { 4 } \\ 0 \\ \frac { 21 } { 4 } \end{array} \right]$
D)
$\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } - \frac { 9 } { 4 } \\ \frac { 3 } { 4 } \\ 0 \\ \frac { 3 } { 2 } \end{array} \right]$


E) $\left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \\ x _ { 4 } \end{array} \right] = \left[ \begin{array} { c } 0 \\ - \frac { 3 } { 4 } \\ 0 \\ - \frac { 3 } { 2 } \end{array} \right]$