(Solved): The augmented matrix is given for a system of equations. If the system is consistent, find the gen ...

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. \[ \left[\begin{array}{rrrr} 1 & 0 & 6 & 2 \\ 0 & 1 & -2 & -3 \\ 0 & 0 & 0 & 0 \end{array}\right] \] \[ x_{1}=2-6 x_{3} \] \( x_{2} \) is free \[ x_{3}=\frac{3}{2}+\frac{1}{2} x_{2} \] \[ \begin{array}{l} x_{1}=2-6 x_{3} \\ x_{2}=-3+2 x_{3} \end{array} \] \( x_{3} \) is free No solution \[ \begin{array}{l} x_{1}=2-6 x_{3} \\ x_{2}=-3+2 x_{3} \\ x_{3}=0 \end{array} \] Question 6 \( 1 \mathrm{pts} \) Solve the problem. Let \( \mathrm{v}_{1}=\left[\begin{array}{c}1 \\ -3 \\ -4\end{array}\right], \mathrm{v}_{2}=\left[\begin{array}{c}-3 \\ 8 \\ 4\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}2 \\ -2 \\ 6\end{array}\right] \). Determine if the set \( \left\{\mathrm{v}_{1}, \mathrm{v}_{2}, \mathrm{v}_{3}\right\} \) is linearly independent. Yes No