Answer
singular
Work Step by Step
Since one can show that
$$\left|\begin{array}{rrr} 2&-1/2&8\\ 1&-1/4&4
\\ -5/2&3/2&8
\end{array}\right|=0,$$
then the matrix
$$\left[\begin{array}{rrr} 2&-1/2&8\\ 1&-1/4&4
\\ -5/2&3/2&8\end{array}\right]$$
is singular.
