Answer
nonsingular
Work Step by Step
Since one can see easily that
$$\left|\begin{array}{rrr} 0.8& 0.2&- 0.6& 0.1\\
- 1.2& 0.6& 0.6&0\\ 0.7&- 0.3& 0.1&0
\\ 0.2&- 0.3& 0.6&0
\end{array}\right|=0.015,$$
then the matrix
$$\left[\begin{array}{rrr} 0.8& 0.2&- 0.6& 0.1\\
- 1.2& 0.6& 0.6&0\\ 0.7&- 0.3& 0.1&0
\\ 0.2&- 0.3& 0.6&0\end{array}\right]$$
is nonsingular.
