Answer
$$x_1=0,\quad x_2= -\frac{1}{7}, \quad x_3=\frac{3}{7}.$$
Work Step by Step
We have the system
$$\left[ \begin {array}{ccc} 0&1&-2\\ -1&3&1
\\ 2&-2&4\end {array} \right]
\left[\begin{array}{rrr}{x_1}\\ {x_2} \\{x_3} \end{array}\right]=\left[\begin{array}{rrr}{-1} \\ {0}\\{2} \end{array}\right].$$
The coefficients matrix $A= \left[ \begin {array}{ccc} 0&1&-2\\ -1&3&1
\\ 2&-2&4\end {array} \right]
$ has the inverse
$$A^{-1}=\left[ \begin {array}{ccc} 1&0&\frac{1}{2}\\ \frac{3}{7}&\frac{2}{7}&\frac{1}{7}
\\ -\frac{2}{7}&\frac{1}{7}&\frac{1}{14}\end {array} \right]
.
$$
The system has the solution
$$\left[\begin{array}{rrr}{x_1}\\ {x_2} \\{x_3} \end{array}\right]=\left[ \begin {array}{ccc} 1&0&\frac{1}{2}\\ \frac{3}{7}&\frac{2}{7}&\frac{1}{7}
\\ -\frac{2}{7}&\frac{1}{7}&\frac{1}{14}\end {array} \right]\left[\begin{array}{rrr}{-1} \\ {0}\\{2} \end{array}\right]=\left[ \begin {array}{c} 0\\ -\frac{1}{7}
\\ \frac{3}{7}\end {array} \right]
.$$
That is
$$x_1=0,\quad x_2= -\frac{1}{7}, \quad x_3=\frac{3}{7}.$$
