Find the rank of the following matrix: \begin{bmatrix} 1 & 0 & 1 & 1 & 2\\ -1 & 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 1 & 1\\ 1 & 0 & 1 & 1 & 2\\ \end{bmatrix}

Find the rank of the following matrix:

$\begin{bmatrix} 1 & 0 & 1 & 1 & 2\\ -1 & 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 1 & 1\\ 1 & 0 & 1 & 1 & 2\\ \end{bmatrix}$

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