Answer
$$
\left[ \begin {array}{cccc} 1&2&1&-1\\ 0&1&0&2\\0&0&-1&-5\\0&0&0&-19\end{array} \right]=19.
$$
Work Step by Step
Given
$$
\left[ \begin {array}{cccc} 1&2&1&-1\\ 0&1&0&2\\0&3&-1&1\\0&0&4&1\end{array} \right].
$$
Now, multiplying the second row by $-3$ and adding it to the third row, we get
$$
\left[ \begin {array}{cccc} 1&2&1&-1\\ 0&1&0&2\\0&0&-1&-5\\0&0&4&1\end{array} \right].
$$
Multiplying the third row by $4$ and adding it to the fourth row, we get
$$
\left[ \begin {array}{cccc} 1&2&1&-1\\ 0&1&0&2\\0&0&-1&-5\\0&0&0&-19\end{array} \right].
$$
Hence, it is very easy to note that
$$
\left[ \begin {array}{cccc} 1&2&1&-1\\ 0&1&0&2\\0&0&-1&-5\\0&0&0&-19\end{array} \right]=19.
$$
