\[\begin{bmatrix} 1 & 0 & 1 & 1\\ 2& -1 & -1 & 1\\ 2& 5 & 3 & 0\\ 1& -1 & 0 & 1 \end{bmatrix}= \begin{bmatrix} -1 & -1 & 1\\ 5 & 3 & 0\\ -1& 0 & 1 \end{bmatrix}-0+1 \begin{bmatrix} 2 & -1 &1 \\ 2 & 5 & 0\\ 1& -1& 1 \end{bmatrix}-1 \begin{bmatrix} 2 & -1 & -1\\ 2& 5 & 3\\ 1& -1 & 0 \end{bmatrix}\]
\[=5-0+5-10 =0\]
A = matrix(c(1,2,2,1,0,-1,5,-1,1,-1,3,0,1,1,0,1),4,4)
det(A)## [1] 7.771561e-16