\(A=\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\end{bmatrix}\)
\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (Applying R3 → R3 - R2 & R2 → 2R2 - R1)
\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&0&33&22\end{bmatrix}\) (Applying R3 → 5R3 + 4R2)
∴ Rank of given matrix is 3.