1. Convert the following system of equations to an augmented matrix and perform row reduction to bringit to reduced echelon form. In your reduced echelon matrix, circle all pivot positions.

Then determinethe solution set for the system. If there are infinitely many solutions, then label which variables are free and solve for the others. Thengive three examples of solutions. \text { (a) }\left\{\begin{array}{l} x_{1}+5 x_{2}=7 \\ 3 x_{1}-x_{2}=5 \end{array}\right. \text { (b) }\left\{\begin{array}{l} x_{1}+2 x_{2}+4 x_{3}=6 \\ -2 x_{1}+x_{2}-3 x_{3}=-2 \\ x_{2}+x_{3}=3 \end{array}\right. \text { (c) }\left\{\begin{array}{l} 3 x_{1}+x_{2}-x_{3}=8 \\ 2 x_{1}+4 x_{3}=6 \\ x_{1}+x_{2}-5 x_{3}=2 \end{array}\right.