Find the general solution to the augmented matrix:
\[\begin{bmatrix} -6 & 0 & -24 & -6 \\ 0 & -1 & 3 & -5 \\ -8 & 4 & -44 & 12 \end{bmatrix}.\]Click for answer
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\[ \begin{bmatrix} -6 & 0 & -24 & -6 \\ 0 & -1 & 3 & -5 \\ -8 & 4 & -44 & 12 \end{bmatrix} \]Solution:
\begin{solution} Reduced Row Echelon Form: \[\begin{bmatrix} 1 & 0 & 4 & 1 \\ 0 & 1 & -3 & 5 \\ 0 & 0 & 0 & 0 \end{bmatrix}\] General Solution: \[ \begin{bmatrix} x_{ 1 } \\ x_{ 2 } \\ x_{ 3 } \\ \end{bmatrix} = \qquad \begin{bmatrix} 1 \\ 5 \\ 0 \end{bmatrix} \qquad + x_3 \begin{bmatrix} -4 \\ 3 \\ 1 \end{bmatrix} \] \end{solution}