Problem:
Compute the rank of
$\left(
\begin{array}{ccccc}
 \frac{39}{4} & \frac{27}{4} & \frac{15}{2} & -\frac{5}{2} & \frac{7}{4} \\
 \frac{13}{2} & \frac{1}{2} & -\frac{21}{4} & \frac{1}{4} & -\frac{39}{4} \\
 \frac{9}{2} & \frac{19}{4} & -\frac{27}{4} & -\frac{23}{4} & 8 \\
 \frac{19}{2} & 5 & -10 & -\frac{13}{2} & -\frac{9}{4} \\
\end{array}
\right)$.
Answer:
$4$
{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/rank_and_nullity/21835.txt'}