Solve the System of Linear Equations Using the Inverse Matrix

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l l } 5 x _ { 1 } - 10 x _ { 2 } - 5 x _ { 3 } - 10 x _ { 4 } & = 0 \\15 x _ { 1 } - 25 x _ { 2 } - 10 x _ { 3 } - 15 x _ { 4 } & = 8 \\10 x _ { 1 } - 25 x _ { 2 } - 10 x _ { 3 } - 25 x _ { 4 } & = - 8 \\- 5 x _ { 1 } + 20 x _ { 2 } + 20 x _ { 3 } + 55 x _ { 4 } & = 16\end{array} \right.$ using the inverse matrix $\frac { 1 } { 5 } \left[ \begin{array} { c c c c } - 24 & 7 & 1 & - 2 \\- 10 & 3 & 0 & - 1 \\- 29 & 7 & 3 & - 2 \\12 & - 3 & - 1 & 1\end{array} \right]$ .

A) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 } \\x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } \frac { 16 } { 5 } \\\frac { 8 } { 5 } \\\frac { - 8 } { 5 } \\\frac { - 16 } { 5 }\end{array} \right]$
B) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 } \\x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } 0 \\\frac { 8 } { 5 } \\0 \\\frac { 16 } { 5 }\end{array} \right]$
C) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 } \\x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } \frac { 16 } { 5 } \\\frac { 8 } { 5 } \\0 \\0\end{array} \right]$
D) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 } \\x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } \frac { 24 } { 5 } \\\frac { - 8 } { 5 } \\0 \\\frac { - 16 } { 5 }\end{array} \right]$
E) $\left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 } \\x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } \frac { 24 } { 5 } \\\frac { - 8 } { 5 } \\\frac { - 16 } { 5 } \\\frac { 16 } { 5 }\end{array} \right]$