## College Algebra 7th Edition

Start with the augmented matrix, row reduce to reduced row echelon form (Gauss-Jordan.) $\left[\begin{array}{llll} 1 & -1 & 3 & 3\\ 4 & -8 & 32 & 24\\ 2 & -3 & 11 & 4 \end{array}\right]\rightarrow\left(\begin{array}{l} .\\ -4R_{1}.\\ -2R_{1}. \end{array}\right)$ $\rightarrow\left[\begin{array}{llll} 1 & -1 & 3 & 3\\ 0 & -4 & 20 & 12\\ 0 & -1 & 5 & -2 \end{array}\right]\rightarrow\left(\begin{array}{l} +R_{3}.\\ \div(-4).\\ . \end{array}\right)$ $\rightarrow\left[\begin{array}{llll} 1 & 0 & 8 & 1\\ 0 & 1 & -5 & -3\\ 0 & -1 & 5 & -2 \end{array}\right]\rightarrow\left(\begin{array}{l} .\\ .\\ +R_{2}. \end{array}\right)$ $\rightarrow\left[\begin{array}{llll} 1 & 0 & 8 & 1\\ 0 & 1 & -5 & -3\\ 0 & 0 & 0 & -5 \end{array}\right]$ The last row represents the equation $0=-5,$ which is never true - there are no solutions to the system. Inconsistent (no solution).