## Precalculus: Mathematics for Calculus, 7th Edition

$(3,1,2)$
Write the augmented matrix and, using row transformations, arrive at the row-reduced echelon form. $\left[\begin{array}{llll} 0 & 2 & 1 & 4\\ 1 & 1 & 0 & 4\\ 3 & 3 & -1 & 10 \end{array}\right]$ Swap rows 1 and 2, $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 1 & 4\\ 3 & 3 & -1 & 10 \end{array}\right] \ \ \begin{array}{l} .\\ .\\ R_{3}-3R_{1}\rightarrow R_{3}. \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 1 & 4\\ 0 & 0 & -1 & -2 \end{array}\right] \ \ \begin{array}{l} .\\ +R_{3}.\\ \times(-1). \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 0 & 2\\ 0 & 0 & 1 & 2 \end{array}\right]\ \ \begin{array}{l} .\\ \div 2.\\ . \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 2 \end{array}\right]\ \ \begin{array}{l} -R_{2}.\\ .\\ . \end{array}$ $\left[\begin{array}{llll} 1 & 0 & 0 & 3\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 2 \end{array}\right]$ Solution: $(3,1,2)$