Consider the system $$\left\lbrace \begin{array}{rcr} x_{1}-2x_{2}-2x_{3} & = & 2 \\ 3x_{1}+3x_{2}-x_{3} & = & 2 \\ 2x_{1}+x_{2}+3x_{3} & = & -1 \end{array} \right.$$ (a) Find the reduced row echelon form of the augmented matrix for this system. Your answers must be fractions (decimals are not allowed). You should be able to do this exercise without a calculator.

$\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.

(b) Solve the original system of equations. Your answers must be fractions (decimals are not allowed).

$\vec{x} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.