Answer
singular
Work Step by Step
Since one can see easily that
$$\left|\begin{array}{rrr} 1&0&-8&2\\ 0&8&-1&10
\\ 0&0&0&1\\0&0&0&2
\end{array}\right|=0,$$
then the matrix
$$\left[\begin{array}{rrr} 1&0&-8&2\\ 0&8&-1&10
\\ 0&0&0&1\\0&0&0&2\end{array}\right]$$
is singular.
