\(A=\begin{bmatrix}1&-1&2&-3\\4&1&0&2\\0&3&0&4\\0&1&0&2\end{bmatrix}\)

↔ \(\begin{bmatrix}2&1&-1&-3\\0&4&1&2\\0&0&3&4\\0&0&1&2\end{bmatrix}\)

(Applying C_{1} ↔ C_{3} Then C_{2} ↔ C_{3})

↔\(\begin{bmatrix}2&1&-1&-3\\0&4&1&2\\0&0&3&4\\0&0&0&2\end{bmatrix}\) (Applying R_{4} → 3R_{4} - R_{3})

∴ Rank of matrix A is 4.