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find rank of Matix \[ A=\left[\begin{array}{rrrr} 2 & 3 & -1 & -1 \\ 1 & -1 & -2 & -4 \\ 3 & 1 & 3 & -2 \end{array}\right] \]

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

\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (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 R→ 5R3 + 4R2)

∴ Rank of given matrix is 3.

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