Answer
$\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$
Work Step by Step
We will add $R_1$ to $R_2$, subtract $R_1$ from row $3$ and subtract $3R_1$ from $R_4$.
We have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &1 & 0 & -1 \\ 0 & 2& 0 & -2 \end{bmatrix}$
Now, we subtract $R_2$ from $R_3$ and $2 R_2$ from $R_4$.
We have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$
Finally, we have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$
