Solve the system of linear equations
$$\left\{ \begin{array} { l }
6 x _ { 1 } - 12 x _ { 2 } - 6 x _ { 3 } - 12 x _ { 4 } = 0 \
18 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 18 x _ { 4 } = - 3 \
12 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 30 x _ { 4 } = 2 \
- 6 x _ { 1 } + 24 x _ { 2 } + 24 x _ { 3 } + 66 x _ { 4 } = 0 \
{ \left[ \begin{array} { c c c c }
- 24 & 7 & 1 & - 2 \
- 10 & 3 & 0 & - 1 \
- 29 & 7 & 3 & - 2 \
12 & - 3 & - 1 & 1
\end{array} \right] }
\end{array} \right.$$
A)
$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c }
- \frac { 19 } { 6 } \
- \frac { 3 } { 2 } \
- \frac { 5 } { 2 } \
\frac { 7 } { 6 }
\end{array} \right]$
B)
$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c }
- \frac { 7 } { 6 } \
- \frac { 5 } { 6 } \
\frac { 3 } { 2 } \
- \frac { 3 } { 2 }
\end{array} \right]$
C)
$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c }
- \frac { 3 } { 2 } \
- \frac { 19 } { 6 } \
0 \
\frac { 7 } { 6 }
\end{array} \right]$
D)
$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c }
- \frac { 1 } { 2 } \
\frac { 1 } { 6 } \
0 \
\frac { 1 } { 3 }
\end{array} \right]$
E)
$\left[ \begin{array} { l }
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c }
0 \
- \frac { 1 } { 6 } \
0 \
- \frac { 1 } { 3 }
\end{array} \right]$

Question

Solve the system of linear equations
$$\left\{ \begin{array} { l } 
6 x _ { 1 } - 12 x _ { 2 } - 6 x _ { 3 } - 12 x _ { 4 } = 0 \
18 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 18 x _ { 4 } = - 3 \
12 x _ { 1 } - 30 x _ { 2 } - 12 x _ { 3 } - 30 x _ { 4 } = 2 \
- 6 x _ { 1 } + 24 x _ { 2 } + 24 x _ { 3 } + 66 x _ { 4 } = 0 \
{ \left[ \begin{array} { c c c c } 
- 24 & 7 & 1 & - 2 \
- 10 & 3 & 0 & - 1 \
- 29 & 7 & 3 & - 2 \
12 & - 3 & - 1 & 1
\end{array} \right] }
\end{array} \right.$$
A)
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 19 } { 6 } \
- \frac { 3 } { 2 } \
- \frac { 5 } { 2 } \
\frac { 7 } { 6 }
\end{array} \right]$
B)
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 7 } { 6 } \
- \frac { 5 } { 6 } \
\frac { 3 } { 2 } \
- \frac { 3 } { 2 }
\end{array} \right]$
C)
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 3 } { 2 } \
- \frac { 19 } { 6 } \
0 \
\frac { 7 } { 6 }
\end{array} \right]$ 
D)
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
- \frac { 1 } { 2 } \
\frac { 1 } { 6 } \
0 \
\frac { 1 } { 3 }
\end{array} \right]$
E)
$\left[ \begin{array} { l } 
x _ { 1 } \
x _ { 2 } \
x _ { 3 } \
x _ { 4 }
\end{array} \right] = \left[ \begin{array} { c } 
0 \
- \frac { 1 } { 6 } \
0 \
- \frac { 1 } { 3 }
\end{array} \right]$

Quizplus · Accepted Answer

The system of linear equations is consistent and has a unique solution. The solution is:$\left[ \begin{array} { l } x _ { 1 } \x _ { 2 } \x _ { 3 } \x _ { 4 }\end{array} \right] = \left[ \begin{array} { c } - \frac { 19 } { 6 } \- \frac { 3 } { 2 } \- \frac { 5 } { 2 } \\frac { 7 } { 6 }\end{array} \right]$

Solve the System of Linear Equations A) B) C) D)